simplify 1/(x+yi)

Solution

simplify

\frac{1}{x + y i}

\frac{x}{x ^{2} + y ^{2}} - \frac{y}{x ^{2} + y ^{2}} i

Solution steps

\frac{1}{x + y i}

Multiply by the conjugate

\frac{x - y i}{x - y i}

= \frac{1 \cdot ( x - y i )}{( x + y i ) ( x - y i )}

Simplify

\frac{1 \cdot ( x - y i )}{( x + y i ) ( x - y i )} : \frac{x - y i}{x ^{2} + y ^{2}}

= \frac{x - y i}{x ^{2} + y ^{2}}

Rewrite in standard complex form:

\frac{x}{x ^{2} + y ^{2}} - \frac{y}{x ^{2} + y ^{2}} i

= \frac{x}{x ^{2} + y ^{2}} - \frac{y}{x ^{2} + y ^{2}} i

y^{3} - y^{2} + y - 1

9 z^{2} - 4

\frac{1}{7} + \frac{1}{8}

3 x^{2} + 18 x = 0

(\frac{2 a ^{6} \cdot 2 a ^{5} b ^{4}}{2 a ^{3}})^{3}