5
QuizMultiple Choice

Powers and Roots of Complex Numbers — Unit test

Question 5 • Precalculus

Let z = 19 + i and w = 4 + 10i.What is the first step in determining zw?

Answer
A
Replace i2 with –1.
B
Multiply z by the conjugate of w.
C
Apply the distributive property or FOIL.
D
Combine the corresponding real and imaginary parts.

Explanation

To multiply z = 19 + i and w = 4 + 10i, start by multiplying each term in one binomial by each term in the other using the distributive property (FOIL). This produces terms including i²; replacing i² with −1 happens afterward. So the first step is to apply the distributive property or FOIL.

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