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Chapter 11: Problem 27

When \(i^{2}\) appears in an expression, it should be replaced with what?

Short Answer

Expert verified
When \(i^2\) appears in an expression, it should be replaced with \(-1\).

Step by step solution

01

Definition of i in complex numbers

The imaginary unit, denoted as \(i\), is defined as the square root of -1. In other words, \(i = \sqrt{-1}\).
02

Computing i^2

To find \(i^2\), simply square the definition of \(i\): \(i^2 = (\sqrt{-1})^2\).
03

Simplifying the expression

When we square the square root of a number, we're left with the number itself (i.e., the square and square root undo each other): \(i^2 = -1\). So, when you see \(i^2\) in an expression, you should replace it with -1.

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