Let `z=costheta+isin theta`, where `i=sqrt(-1)`. Then the value of `sum_(m=1)^(15)Im(z^(2m-1))` at `theta=2^(@)` is

Let z=costheta+isintheta . Then the value of sum_(m->1-15)Img(z^(2m-1)) at theta=2^@ is:

If a = cos theta + isin theta , then find the value of (1 +a)/(1-a) .

If z = 1 -cos theta+ isin theta then |z| is equal to

If z= costheta+isintheta , then the value of (z^(2n)-1)/(z^(2n)+1) (A) i tan n theta (B) tan n theta (C) icot n theta (D) -i tan n theta

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

If pi < theta < 2pi and z=1+cos theta + i sin theta , then write the value of |z|

Let z=9+ai, where i=sqrt(-1) and a be non-zero real. If Im(z^(2))=Im(z^(3)) , sum of the digits of a^(2) is

Let f (theta)=(1)/(1+(tan theta)^(2021)) , then the value of sum_(theta=1^(@))^(89^(@))f(theta) is equal to

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Find the value of Im(z) .

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .