SOLUTION: 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 =

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 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 =       Log On


   

Question 1085359: 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=1+3i, find I. Express your answer as a complex number in the form a+bi, where a and b are real numbers.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
1-i=I(1+3i)
I = (1-i)/(1+3i)
multiply numerator and denominator by conjugate 1-3i. The denominator will become 1-9*i^2=1+9=10
The numerator will be expanded to be 1-3i-i+3i^2=1-4i-3=-2-4i
This is -2-4i/10
divide numerator and denominator by -2
-(1+2i)/5