# Math Help - Multiplicative Inverse of...

1. ## Multiplicative Inverse of...

First off, if z = x + yi with x,y e R
then, (z) = x - yi with x,y e R (It's the complex conjugate)

Now, let w = [(z)z]^(-1)[(z)]

Use the above formula for w to find the multiplicative inverse of z = 2 + i. Answers to be in the form a + bi with a,b e R.

2. you are interested in finding $(2+i)^{-1}$.
$(2+i)^{-1}=\frac{1}{2+i}=\frac{1}{2+i}\frac{2-i}{2-i}=\frac{2-i}{5}=\frac{2}{5}-\frac{1}{5}i$