tentukan bilangan real dan imajiner 1. √2 e pangkat 5i pi/4 2. (1+i) pangkat 2 + (1 +i ) pangkat 4

[tex]1. \\ $Identitas Euler:$ \\ e^{ix}=\cos x + i \sin x \\ \sqrt{2}e^{i\times\frac{5\pi}{4}}=\sqrt{2}(\cos(\frac{5\pi}{4})+i\sin(\frac{5\pi}{4})) \\ \sqrt{2}(-\frac{1}{\sqrt{2}}- i\frac{1}{\sqrt{2}}) \\ -1-i \\ Re(x)=-1 \\ Im(x)=-i \\ \\ 2. \\ (1+i)^2+(1+i)^4 \\ (1+2i-1) + (1+2i-1)^2 \\ 2i + (2i)^2 \\ -4+2i \\ Re(x)=-4 \\ Im(x)=2i[/tex]