Respuesta :

[tex]\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[/tex]
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ANSWER


[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]


EXPLANATION


The given expression is


[tex](5 - 2 {i}^{2} ) ^{2} [/tex]


This is an expression containing a complex number.



Recall that in complex numbers,

[tex] {i}^{2} = - 1[/tex]

The expression now becomes,


[tex](5 - 2 {i}^{2} ) ^{2} = (5 - 2 ( - 1) ) ^{2} [/tex]


This implies that,


[tex](5 - 2 {i}^{2} ) ^{2} = (5 + 2 ) ^{2} [/tex]



This will simplify to,


[tex](5 - 2 {i}^{2} ) ^{2} = {7}^{2} [/tex]


This eventually gives us,



[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

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