If `z=r e^(itheta)` , then prove that `|e^(i z)|=e^(-r sintheta)`

If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r s inthetadot)

If z=re^(itheta) then |e^(iz)| is equal to:

If z=(a+i b)^5+(b+i a)^5 , then prove that R e(z)=I m(z),w h e r ea ,b in Rdot

If z=4 + 3i , then verify that -|z| le R e (z) lt |z|

Find the real part of e^e^(itheta)

If sintheta+costheta=m , then prove that sin^6theta+cos^6theta=(4-3(m^2-1)^2)/4,\ w h e r e\ m^2lt=2.

If |z-i R e(z)|=|z-I m(z)| , then prove that z , lies on the bisectors of the quadrants.

If |z-i R e(z)|=|z-I m(z)| , then prove that z , lies on the bisectors of the quadrants.

let z1, z2,z3 be vertices of triangle ABC in an anticlockwise order and angle ACB = theta then z_2-z_3 = (CB)/(CA)(z_1-z3) e^itheta . let p point on a circle with op diameter 2 points Q & R taken on a circle such that angle POQ & QOR= theta if O be origin and PQR are complex no. z1, z2, z3 respectively then z_2/z_1 = (A) e^(itheta) cos theta (B) e^(itheta) cos 2theta (C) e^(-itheta) cos theta (D) e^(2itheta) cos 2theta

If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.