Question

just to check my math,
cos pi/10 = .95
sin pi/10 =.31

Answer 1

\[[\frac{ 1 }{ 4 }(\cos \frac{ \pi }{ 10 }+i \sin \frac{ \pi }{ 10 })]^{5}\]

Answer 2

there is a theorem we can use

Answer 3

( r cos theta + i sin theta ) ^n = r^n * cos (theta*n ) + i sin (thetan * n )

Answer 4

i found something like this,
\[\frac{ 1 }{ 4 }^{5}(\cos (5*\frac{ \pi }{10}+i \sin (5*\frac{ \pi }{ 10 })\]

Answer 5

yes thats right

Answer 6

here is my findings,
.000976(.000796)+i(.999)

Answer 7

what is cos(pi/2) ?

Answer 8

cos (5pi/10) = cos(pi/2) = 0

Answer 9

where did cos(pi/2)come from

Answer 10

5pi/10 = pi/2

Answer 11

so disregard my last equation,
\[\frac{ 1 }{ 4 }^{5}(\cos \frac{ \pi }{ 2}+isin \frac{ \pi }{ 2 })\]

Answer 12

\[\frac{ 1 }{ 4 }^{5}(0+i*1)\]

Answer 13

final answer would be
\[\frac{ 1 }{1024 }i\]