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

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Dayton

Business

14 April, 14:34

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

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Abigayle Archer · 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