Simplify (2(1-i square root of 2)-3)/((1-i square root of 2)^2)

$\frac{2 (1 - i \sqrt{2}) - 3}{{(1 - i \sqrt{2})}^{2}}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 \cdot 1 + 2 (- i \sqrt{2}) - 3}{{(1 - i \sqrt{2})}^{2}}$

Multiply $2$ by $1$ .

$\frac{2 + 2 (- i \sqrt{2}) - 3}{{(1 - i \sqrt{2})}^{2}}$

Multiply $- 1$ by $2$ .

$\frac{2 - 2 (i \sqrt{2}) - 3}{{(1 - i \sqrt{2})}^{2}}$

Subtract $3$ from $2$ .

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

Rewrite ${(1 - i \sqrt{2})}^{2}$ as $(1 - i \sqrt{2}) (1 - i \sqrt{2})$ .

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

Expand $(1 - i \sqrt{2}) (1 - i \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

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

Multiply $- i \sqrt{2}$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Multiply $- i \sqrt{2} (- i \sqrt{2})$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\sqrt{2}$ by $1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

Multiply $2$ by $- 1$ .

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

Subtract $2$ from $1$ .

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

Subtract $i \sqrt{2}$ from $- i \sqrt{2}$ .

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

Reorder $- 2 i \sqrt{2}$ and $- 1$ .

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

Cancel the common factor of $- 2 i \sqrt{2} - 1$ and $- 1 - 2 i \sqrt{2}$ .

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$1$

Simplify (2(1-i square root of 2)-3)/((1-i square root of 2)^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.