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=(1+i)/(2-i)=((1+i)(2+i))/((2-i)(2+i))=(2+i+2i+i^2)/(2^2-i^2)=(2+3i-1)/(4-(-1))=(1+3i)/(5)\\\\\\\\\boxed{I=(1+3i)/(5)=(1)/(5)+(3)/(5)i}`