Answer:
The real solution is [tex]n=6[/tex].
Step-by-step explanation:
[tex]\cos(\frac{\pi}{2})=0[/tex] while [tex]\sin(\frac{\pi}{2})=1[/tex]
So the equation becomes:
[tex]-64=(2(0)+2i(1))^n[/tex]
[tex]-64=(0+2i)^n[/tex]
[tex]-64=(2i)^n[/tex]
We know that [tex]2^6=64[/tex]. So let's see what [tex]n=6[/tex] gives us:
[tex](2i)^6=64i^6=64i^4i^2=64(1)(-1)=-64[/tex].
[tex]-64[/tex] is the result we wanted.
[tex]n=6[/tex] is therefore a solution.
