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# Help

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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.

Jun 20, 2019

### Best Answer

#1
+91
+2

So, we can plug the variables into the equation.

$$1- i = (1+3i) I.$$

We divide 1 + 3i on both sides to get:

$$\frac{1-i}{1+3i} = I$$

Then we multiply 1-3i on the numerator and the denominator of the left side to get:

$$-\frac12-i$$.

So, $$I = -\frac12-i$$

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Jun 20, 2019

### 4+0 Answers

#1
+91
+2
Best Answer

So, we can plug the variables into the equation.

$$1- i = (1+3i) I.$$

We divide 1 + 3i on both sides to get:

$$\frac{1-i}{1+3i} = I$$

Then we multiply 1-3i on the numerator and the denominator of the left side to get:

$$-\frac12-i$$.

So, $$I = -\frac12-i$$

Pushy Jun 20, 2019
#2
+102937
0

Good job  !!!!

CPhill  Jun 20, 2019
#3
+91
+1

Thanks :)

Pushy  Jun 20, 2019
#5
0

Wait is this in the correct format?

Jun 21, 2019