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 $Z=1+3i$, find $I$. Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers

Answer 1

Answer: I=-1/5-2/5i

Explanation: V=IZ

1-i=I(1+3i)

Make I subject

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 I= (-2-4i)/10

divide numerator and denominator by -2. We have:

I=-(1+2i)/5

I=-1/5-2/5i