Question

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

Answer 1

`\bf (5-2i^2)^2\qquad \textit{now recall }i^2=√(-1)\cdot √(-1)=√((-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`


Step-by-step 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`