Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises: 4

Answer

True

Work Step by Step

The statement "A number can be both real and complex" is true. It is because, for any complex number $z$ = $a + bi$, when the imaginary part $b = 0$, $z$ will be equal to $a$, which is real and complex (since real is a subset of complex). And, in case of both $a$ and $b$ equal to $0$, $z$ will be equal to $0$, which is both real and complex as well. The only exception is when $a$ = $0$, $z$ will be equal to $bi$, which is not real but just pure imaginary. With this exception, it cannot be real but just complex only.
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