What is simplify+1/(a+bi) ?

The solution to simplify+1/(a+bi) is a/(a^2+b^2)-b/(a^2+b^2)i

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simplify+1/(a+bi)

simplify

+ \frac{1}{a + bi}

\frac{a}{a ^{2} + b ^{2}} - \frac{b}{a ^{2} + b ^{2}} i

Solution steps

\frac{1}{a + bi}

Multiply by the conjugate

\frac{a - bi}{a - bi}

= \frac{1 \cdot ( a - bi )}{( a + bi ) ( a - bi )}

Simplify

\frac{1 \cdot ( a - bi )}{( a + bi ) ( a - bi )} : \frac{a - bi}{a ^{2} + b ^{2}}

= \frac{a - bi}{a ^{2} + b ^{2}}

Rewrite in standard complex form:

\frac{a}{a ^{2} + b ^{2}} - \frac{b}{a ^{2} + b ^{2}} i

= \frac{a}{a ^{2} + b ^{2}} - \frac{b}{a ^{2} + b ^{2}} i

5^{8} + 1. 4^{5}

(- 2 x^{2} + 5 x) - (8 x^{2} + x - 4)

3 x^{2} - 12 x y

6 x^{3} - 33 x^{2} + 45 x - 6

24 \cdot 6

What is simplify+1/(a+bi) ?
The solution to simplify+1/(a+bi) is a/(a^2+b^2)-b/(a^2+b^2)i