Chapter A.7, Problem 1AYU

To determine

To find: Whether the statement is true or false.

Answer to Problem 1AYU

The statement is true.

Explanation of Solution

Given information:

The given statement is “ The square of a complex number is sometimes negative "".

Calculation:

Consider s complex number $9i^4$ .

Square the assumed number.

$\begin{array}{c}\text{square}={\left(3i\right)}^2\\ =9i^2\\ =9\left(-1\right)\left(-1\right)\\ =9\end{array}$

The result here is positive.

Let us assume another complex number $i$ .

Square the assumed number.

$\begin{array}{c}\text{square}=i^2\\ =-1\end{array}$

Here the square of complex number is negative.

Therefore, the given statement is true.