Question

Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation V = IZ, V is voltage, I is current, and Z is a value known as impedance. If V = 1+i and Z=2-i, find I. Please do this quickly!!

Answer 1

$V=IZ\\\\1+i=I\cdot(2-i)\quad|:(2-i)\\\\\\I=\dfrac{1+i}{2-i}=\dfrac{(1+i)(2+i)}{(2-i)(2+i)}=\dfrac{2+i+2i+i^2}{2^2-i^2}=\dfrac{2+3i-1}{4-(-1)}=\dfrac{1+3i}{5}\\\\\\\\\boxed{I=\frac{1+3i}{5}=\frac{1}{5}+\frac{3}{5}i}$