Step-by-step explanation:
We have , to simplify a complex expression . Basically a complex expression in the form a + ib , where i = [tex]\sqrt{-1}[/tex] and is called iota.
Expression:
[tex](2+2i)^{8}[/tex]
⇒ [tex](2+2i)^{8}[/tex]
⇒[tex]2^{8}(1+i)^{8}[/tex]
We know that the mod or modulus of a complex number in the form of [tex]a+ib[/tex] is represented by Z and Z = [tex]\sqrt{a^{2}+b^{2}}[/tex] . Computing mod of [tex]1+i[/tex] as :
⇒ [tex]Z = \sqrt{a^{2}+b^{2}}[/tex]
⇒ [tex]Z = \sqrt{1^{2}+1^{2}}[/tex]
⇒ [tex]Z = \sqrt{2}[/tex]
Putting value of [tex]1+i[/tex] as [tex]Z = \sqrt{2}[/tex] , we get:
⇒[tex]2^{8}(1+i)^{8}[/tex]
⇒[tex]2^{8}(\sqrt{2})^{8}[/tex]
⇒[tex]256(2^{4})[/tex]
⇒[tex]4096[/tex]
