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

Real part of (e^e)^(iotatheta) is

Find the real part of (1-i)^(-i)dot

Find the real part of (1-i)^(-i)dot

If the imaginery part of (z-3)/(e^(itheta))+(e^(itheta))/(z-3) is zero, then z can lie on

Statement-1 : If e^(itheta)=cos theta +isintheta and the value of e^(iA).e^(iB).e^(iC) is equal to -1, where A,B,C are the angles of a triangle. and Statement -2 : In any triangleABC , A + B +C = 180^(@)

Find number of real roots of equation e^(4x) + e^(3x) - 4e^(2x) + e^(x) + 1 = 0 is

The amplitude of e^(e^-(itheta)) , where theta in R and i = sqrt(-1) , is

If e^(itheta)=costheta+is intheta, find the value of |1e^(ipi//3)e^(ipi//4)e^(-ipi//3)1e^(i2pi//3)e^(-ipi//4)e^(-i2pi//3)1|

If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e^(ipi//4)],[e^(-ipi//3),1,e^(i2pi//3)],[e^(-ipi//4),e^(-i2pi//3),1]|

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