Question

Perform the indicated operation. (5 - 2i 2) 2

Answer 1

$\bf (5-2i^2)^2\qquad \textit{now recall }i^2=\sqrt{-1}\cdot \sqrt{-1}=\sqrt{(-1)^2}=-1 \\\\\\ (5-2(-1))^2\implies (5+2)^2\implies 7^2\implies 49$

Answer 2

ANSWER


$(5 - 2 {i}^{2} ) ^{2} = 49$


EXPLANATION


The given expression is


$(5 - 2 {i}^{2} ) ^{2}$


This is an expression containing a complex number.



Recall that in complex numbers,

${i}^{2} = - 1$

The expression now becomes,


$(5 - 2 {i}^{2} ) ^{2} = (5 - 2 ( - 1) ) ^{2}$


This implies that,


$(5 - 2 {i}^{2} ) ^{2} = (5 + 2 ) ^{2}$



This will simplify to,


$(5 - 2 {i}^{2} ) ^{2} = {7}^{2}$


This eventually gives us,



$(5 - 2 {i}^{2} ) ^{2} = 49$