Convert to Rectangular 18(cos(315)+isin(315))

$18 (\cos (315) + i \sin (315))$

Step 1

Simplify each term.

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

$18 (\cos (45) + i \sin (315))$

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

$18 (\frac{\sqrt{2}}{2} + i \sin (315))$

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

$18 (\frac{\sqrt{2}}{2} + i (- \sin (45)))$

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

$18 (\frac{\sqrt{2}}{2} + i (- \frac{\sqrt{2}}{2}))$

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

$18 (\frac{\sqrt{2}}{2} - \frac{i \sqrt{2}}{2})$

Step 2

Simplify terms.

Apply the distributive property.

$18 \frac{\sqrt{2}}{2} + 18 (- \frac{i \sqrt{2}}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $18$ .

$2 (9) \frac{\sqrt{2}}{2} + 18 (- \frac{i \sqrt{2}}{2})$

Cancel the common factor.

$2 \cdot 9 \frac{\sqrt{2}}{2} + 18 (- \frac{i \sqrt{2}}{2})$

Rewrite the expression.

$9 \sqrt{2} + 18 (- \frac{i \sqrt{2}}{2})$

Cancel the common factor of $2$ .

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

$9 \sqrt{2} + 18 \frac{- i \sqrt{2}}{2}$

Factor $2$ out of $18$ .

$9 \sqrt{2} + 2 (9) \frac{- i \sqrt{2}}{2}$

Cancel the common factor.

$9 \sqrt{2} + 2 \cdot 9 \frac{- i \sqrt{2}}{2}$

Rewrite the expression.

$9 \sqrt{2} + 9 (- i \sqrt{2})$

Multiply $- 1$ by $9$ .

$9 \sqrt{2} - 9 i \sqrt{2}$

Convert to Rectangular 18(cos(315)+isin(315))

Related Questions

Support LCMGCF.com by disabling your adblocker.