If `Z` is an idempotent matrix, then `(I+Z)^n` `I+2^n Z` b. `I+(2^n-1)Z` c. `I-(2^n-1)Z` d. none of these

If Z is an idempotent matrix,then (I+Z)^(n)I+2^(n)Z b.I+(2^(n)-1)Z c.I-(2^(n)-1)Zd . none of these

If Z is an idempotent matrix, then (I + Z)^(n) a) I + 2^(n)Z b) I+ (2^(n) - 1) Z c) I - (2^(n) - 1) Z d)None of these

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If z=(i)^(i)^(((i)))w h e r e i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

If n is a positive integer, prove that |I m(z^n)|lt=n|Im(z)||z|^(n-1.)

If z=(i)^(i)^(i) where i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

If n is an integer and z=cis theta,(theta ne (2n+1)pi/2), then show that (z^(2n)-1)/(z^(2n)+1)=i tan n theta) .

If n is an integer and z=cos theta+i sin theta , then (z^(2 n)-1)/(z^(2 n)+1)=

If z=(i)^((i)^(i)) w h e r e i=sqrt(-1),t h e n|z| is equal to a. 1 b. e^(-pi//2) c. e^(-pi) d. none of these