Prove on the circle $z=Re^{i\theta},|e^{iz}|=e^{-R\sin{\theta}}$
69020
Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$
140968
Proof for Property of Complex Numbers
60721
How does $e^{i x}$ produce rotation around the imaginary unit circle?
54512
How do I prove: $\cos (\theta + 90^\circ) \equiv - \sin \theta $
52178
Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.
114411
Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
107450
False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
40824
Complex Equation Of a Circle $|z-z_1|^2+|z-z_2|^2=k$.
48394
Proving bessel identity $[J_0(x)]^2 + 2[J_1(x)]^2 + 2[J_2(x)]^2 + \cdots = 1$ and $|J_0(x)|\le 1$
86193
Rigorous proof that $dx dy=r\ dr\ d\theta$
157328
A complex analysis problem to prove an inequality
50038
Proving that $e^\pi=e^{-\pi}$
98282
Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$
38379
Showing that $e^z=z$ has infinitely many solutions
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle