Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.1 - Complex Numbers - Exercise Set - Page 315: 64

Answer

The term $i$ is an imaginary unit which is the solution of the equation ${{x}^{2}}=-1$ and its value is $\sqrt{-1}$.

Work Step by Step

The term is an imaginary unit. The imaginary unit $i$ is the solution of the equation, ${{x}^{2}}=-1$ The square root property is such that if ${{x}^{2}}=k$, then $x=\pm \sqrt{k}$. $x=\pm \sqrt{-1}$ The solution of the equation is $\sqrt{-1}$ and $-\sqrt{-1}$. The solution $\sqrt{-1}$ is called an imaginary unit $i$. $i=\sqrt{-1}\text{ or }{{i}^{2}}=-1$ It expresses the imaginary number or a complex number which is in the form of $a+bi$. Therefore, the term $i$ is an imaginary unit which is the solution of the equation ${{x}^{2}}=-1$ and its value is $\sqrt{-1}$.
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