## Alexis1994_13 4 years ago 1/(x+yi) ,make it like a+bi please. Step by step.

1. Alexis1994_13

x/(x^2+y^2)-yi/(x^2+y^2) is that right ?

2. darthsid

$\frac{1}{x+iy} = \frac{1}{x+iy} \times \frac{x-iy}{x-iy}$ now, multiplying the denominators and using the rule: $(m+n) times (m-n) = m^2 - n^2$ we get: $\frac{1}{x+iy} = \frac{x-iy}{x^2-(iy)^2}$ $\frac{1}{x+iy} = \frac{x-iy}{x^2-i^2y^2}$ $\frac{1}{x+iy} = \frac{x-iy}{x^2-(-1)y^2}$ $\frac{1}{x+iy} = \frac{x-iy}{x^2+y^2}$ $\frac{1}{x+iy} = \frac{x}{x^2+y^2} + i\frac{-y}{x^2+y^2}$