Respuesta :
Answer:a=0
b=32
Step-by-step explanation:
Given
Complex number [tex]z=\left ( 1+i\right )^{10}[/tex]
any complex number is written in the form
[tex]z=re^{i\theta }[/tex]
where r=magnitude
so [tex]z=\left [ \sqrt{2}\left ( \frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}\right )\right ]^{10}[/tex]
[tex]z=\left ( \sqrt{2}\right )^{10}\left ( \cos 45+i\sin 45\right )^{10}[/tex]
[tex]z=2^5\left ( e^{i\frac{\pi }{4}}\right )^{10}[/tex]
[tex]z=32\left ( e^{\frac{5\pi }{2}}\right )[/tex]
[tex]\frac{5\pi }{2}=2\pi +\frac{\pi }{2}[/tex]
[tex]z=32\left ( e^{i\frac{\pi }{2}\right )[/tex]
[tex]z=32\left ( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2}\right )[/tex]
real part [tex]a=32\times \cos (90)=0[/tex]
[tex]b=32\times \sin (90)=32[/tex]
