Convert to Rectangular 5(cos(135 degrees )+isin(135 degrees ))*2(cos(45 degrees )+isin(45 degrees ))

$5 (\cos (135 °) + i \sin (135 °)) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Simplify each term.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$5 (- \cos (45) + i \sin (135 °)) \cdot 2 (\cos (45 °) + i \sin (45 °))$

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$5 (- \frac{\sqrt{2}}{2} + i \sin (135 °)) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$5 (- \frac{\sqrt{2}}{2} + i \sin (45)) \cdot 2 (\cos (45 °) + i \sin (45 °))$

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$5 (- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Combine $i$ and $\frac{\sqrt{2}}{2}$ .

$5 (- \frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Apply the distributive property.

$(5 (- \frac{\sqrt{2}}{2}) + 5 \frac{i \sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Multiply $5 (- \frac{\sqrt{2}}{2})$ .

Multiply $- 1$ by $5$ .

$(- 5 \frac{\sqrt{2}}{2} + 5 \frac{i \sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Combine $- 5$ and $\frac{\sqrt{2}}{2}$ .

$(\frac{- 5 \sqrt{2}}{2} + 5 \frac{i \sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Simplify terms.

Combine $5$ and $\frac{i \sqrt{2}}{2}$ .

$(\frac{- 5 \sqrt{2}}{2} + \frac{5 (i \sqrt{2})}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Move the negative in front of the fraction.

$(- \frac{5 \sqrt{2}}{2} + \frac{5 i \sqrt{2}}{2}) \cdot 2 (\cos (45 °) + i \sin (45 °))$

Simplify terms.

Apply the distributive property.

$(- \frac{5 \sqrt{2}}{2} \cdot 2 + \frac{5 i \sqrt{2}}{2} \cdot 2) (\cos (45 °) + i \sin (45 °))$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 \sqrt{2}}{2}$ into the numerator.

$(\frac{- 5 \sqrt{2}}{2} \cdot 2 + \frac{5 i \sqrt{2}}{2} \cdot 2) (\cos (45 °) + i \sin (45 °))$

Cancel the common factor.

$(\frac{- 5 \sqrt{2}}{2} \cdot 2 + \frac{5 i \sqrt{2}}{2} \cdot 2) (\cos (45 °) + i \sin (45 °))$

Rewrite the expression.

$(- 5 \sqrt{2} + \frac{5 i \sqrt{2}}{2} \cdot 2) (\cos (45 °) + i \sin (45 °))$

Cancel the common factor of $2$ .

Cancel the common factor.

$(- 5 \sqrt{2} + \frac{5 i \sqrt{2}}{2} \cdot 2) (\cos (45 °) + i \sin (45 °))$

Rewrite the expression.

$(- 5 \sqrt{2} + 5 i \sqrt{2}) (\cos (45 °) + i \sin (45 °))$

Simplify each term.

The exact value of $\cos (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$(- 5 \sqrt{2} + 5 i \sqrt{2}) (\frac{\sqrt{2}}{2} + i \sin (45 °))$

The exact value of $\sin (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$(- 5 \sqrt{2} + 5 i \sqrt{2}) (\frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2})$

Combine $i$ and $\frac{\sqrt{2}}{2}$ .

$(- 5 \sqrt{2} + 5 i \sqrt{2}) (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$

Expand $(- 5 \sqrt{2} + 5 i \sqrt{2}) (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$ using the FOIL Method.

Apply the distributive property.

$- 5 \sqrt{2} (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2}) + 5 i \sqrt{2} (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$

Apply the distributive property.

$- 5 \sqrt{2} \frac{\sqrt{2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$

Apply the distributive property.

$- 5 \sqrt{2} \frac{\sqrt{2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $- 5 \sqrt{2} \frac{\sqrt{2}}{2}$ .

Combine $\frac{\sqrt{2}}{2}$ and $- 5$ .

$\frac{\sqrt{2} \cdot - 5}{2} \sqrt{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{\sqrt{2} \cdot - 5}{2}$ and $\sqrt{2}$ .

$\frac{\sqrt{2} \cdot - 5 \sqrt{2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{- 5 ({\sqrt{2}}^{1} \sqrt{2})}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{- 5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 {\sqrt{2}}^{1 + 1}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Add $1$ and $1$ .

$\frac{- 5 {\sqrt{2}}^{2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{- 5 {(2^{\frac{1}{2}})}^{2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 5 \cdot 2^{\frac{1}{2} \cdot 2}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{- 5 \cdot 2^{\frac{2}{2}}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{- 5 \cdot 2^{\frac{2}{2}}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$\frac{- 5 \cdot 2^{1}}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Evaluate the exponent.

$\frac{- 5 \cdot 2}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $- 5$ by $2$ .

$\frac{- 10}{2} - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Divide $- 10$ by $2$ .

$- 5 - 5 \sqrt{2} \frac{i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $- 5 \sqrt{2} \frac{i \sqrt{2}}{2}$ .

Combine $\frac{i \sqrt{2}}{2}$ and $- 5$ .

$- 5 + \frac{i \sqrt{2} \cdot - 5}{2} \sqrt{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{i \sqrt{2} \cdot - 5}{2}$ and $\sqrt{2}$ .

$- 5 + \frac{i \sqrt{2} \cdot - 5 \sqrt{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 + \frac{i \cdot - 5 ({\sqrt{2}}^{1} \sqrt{2})}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 + \frac{i \cdot - 5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 5 + \frac{i \cdot - 5 {\sqrt{2}}^{1 + 1}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Add $1$ and $1$ .

$- 5 + \frac{i \cdot - 5 {\sqrt{2}}^{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Simplify the numerator.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 5 + \frac{i \cdot - 5 {(2^{\frac{1}{2}})}^{2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 5 + \frac{i \cdot - 5 \cdot 2^{\frac{1}{2} \cdot 2}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$- 5 + \frac{i \cdot - 5 \cdot 2^{\frac{2}{2}}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 + \frac{i \cdot - 5 \cdot 2^{\frac{2}{2}}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$- 5 + \frac{i \cdot - 5 \cdot 2^{1}}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Evaluate the exponent.

$- 5 + \frac{i \cdot - 5 \cdot 2}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $2$ by $- 5$ .

$- 5 + \frac{i \cdot - 10}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Move $- 10$ to the left of $i$ .

$- 5 + \frac{- 10 i}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor of $- 10$ and $2$ .

Factor $2$ out of $- 10 i$ .

$- 5 + \frac{2 (- 5 i)}{2} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$- 5 + \frac{2 (- 5 i)}{2 (1)} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor.

$- 5 + \frac{2 (- 5 i)}{2 \cdot 1} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$- 5 + \frac{- 5 i}{1} + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Divide $- 5 i$ by $1$ .

$- 5 - 5 i + 5 i \sqrt{2} \frac{\sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $5 i \sqrt{2} \frac{\sqrt{2}}{2}$ .

Combine $\frac{\sqrt{2}}{2}$ and $5$ .

$- 5 - 5 i + \frac{\sqrt{2} \cdot 5}{2} i \sqrt{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{\sqrt{2} \cdot 5}{2}$ and $i$ .

$- 5 - 5 i + \frac{\sqrt{2} \cdot 5 i}{2} \sqrt{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{\sqrt{2} \cdot 5 i}{2}$ and $\sqrt{2}$ .

$- 5 - 5 i + \frac{\sqrt{2} \cdot 5 i \sqrt{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 - 5 i + \frac{5 i ({\sqrt{2}}^{1} \sqrt{2})}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 - 5 i + \frac{5 i ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 5 - 5 i + \frac{5 i {\sqrt{2}}^{1 + 1}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Add $1$ and $1$ .

$- 5 - 5 i + \frac{5 i {\sqrt{2}}^{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Simplify the numerator.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 5 - 5 i + \frac{5 i {(2^{\frac{1}{2}})}^{2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 5 - 5 i + \frac{5 i \cdot 2^{\frac{1}{2} \cdot 2}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$- 5 - 5 i + \frac{5 i \cdot 2^{\frac{2}{2}}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 - 5 i + \frac{5 i \cdot 2^{\frac{2}{2}}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$- 5 - 5 i + \frac{5 i \cdot 2^{1}}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Evaluate the exponent.

$- 5 - 5 i + \frac{5 i \cdot 2}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $2$ by $5$ .

$- 5 - 5 i + \frac{10 i}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 i$ .

$- 5 - 5 i + \frac{2 (5 i)}{2} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$- 5 - 5 i + \frac{2 (5 i)}{2 (1)} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Cancel the common factor.

$- 5 - 5 i + \frac{2 (5 i)}{2 \cdot 1} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$- 5 - 5 i + \frac{5 i}{1} + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Divide $5 i$ by $1$ .

$- 5 - 5 i + 5 i + 5 i \sqrt{2} \frac{i \sqrt{2}}{2}$

Multiply $5 i \sqrt{2} \frac{i \sqrt{2}}{2}$ .

Combine $\frac{i \sqrt{2}}{2}$ and $5$ .

$- 5 - 5 i + 5 i + \frac{i \sqrt{2} \cdot 5}{2} i \sqrt{2}$

Combine $\frac{i \sqrt{2} \cdot 5}{2}$ and $i$ .

$- 5 - 5 i + 5 i + \frac{i \sqrt{2} \cdot 5 i}{2} \sqrt{2}$

Raise $i$ to the power of $1$ .

$- 5 - 5 i + 5 i + \frac{\sqrt{2} \cdot 5 (i^{1} i)}{2} \sqrt{2}$

Raise $i$ to the power of $1$ .

$- 5 - 5 i + 5 i + \frac{\sqrt{2} \cdot 5 (i^{1} i^{1})}{2} \sqrt{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 5 - 5 i + 5 i + \frac{\sqrt{2} \cdot 5 i^{1 + 1}}{2} \sqrt{2}$

Add $1$ and $1$ .

$- 5 - 5 i + 5 i + \frac{\sqrt{2} \cdot 5 i^{2}}{2} \sqrt{2}$

Combine $\frac{\sqrt{2} \cdot 5 i^{2}}{2}$ and $\sqrt{2}$ .

$- 5 - 5 i + 5 i + \frac{\sqrt{2} \cdot 5 i^{2} \sqrt{2}}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 - 5 i + 5 i + \frac{5 i^{2} ({\sqrt{2}}^{1} \sqrt{2})}{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 5 - 5 i + 5 i + \frac{5 i^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 5 - 5 i + 5 i + \frac{5 i^{2} {\sqrt{2}}^{1 + 1}}{2}$

Add $1$ and $1$ .

$- 5 - 5 i + 5 i + \frac{5 i^{2} {\sqrt{2}}^{2}}{2}$

Simplify the numerator.

Rewrite $i^{2}$ as $- 1$ .

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 {\sqrt{2}}^{2}}{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 {(2^{\frac{1}{2}})}^{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 \cdot 2^{\frac{1}{2} \cdot 2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 \cdot 2^{\frac{2}{2}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 \cdot 2^{\frac{2}{2}}}{2}$

Rewrite the expression.

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 \cdot 2^{1}}{2}$

Evaluate the exponent.

$- 5 - 5 i + 5 i + \frac{5 \cdot - 1 \cdot 2}{2}$

Combine exponents.

Factor out negative.

$- 5 - 5 i + 5 i + \frac{- (5 \cdot 2)}{2}$

Multiply $5$ by $2$ .

$- 5 - 5 i + 5 i + \frac{- 1 \cdot 10}{2}$

Multiply $- 1$ by $10$ .

$- 5 - 5 i + 5 i + \frac{- 10}{2}$

Divide $- 10$ by $2$ .

$- 5 - 5 i + 5 i - 5$

Subtract $5$ from $- 5$ .

$- 10 - 5 i + 5 i$

Add $- 5 i$ and $5 i$ .

$- 10 + 0$

Add $- 10$ and $0$ .

$- 10$

Convert to Rectangular 5(cos(135 degrees )+isin(135 degrees ))*2(cos(45 degrees )+isin(45 degrees ))

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