Proving that a complex number lies on the imaginary axis.
94962
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right)  = 0$
79425
Prove the direct product of nonzero complex numbers under multiplication.
125719
Multiplicative inverse of a complex number.
136721
Absolute value of a complex number proof
141863
If the imaginary part of an entire function is never zero, the function is constant
73687
Powers of $i$ in Complex Numbers.
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
68255
Theorems in complex analysis.
81571
Complex Exponent of Complex Numbers
64076
how to show that this complex series converge?
38674
Do complex numbers really exist?
119628
Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
46701
Complex Number Proof Questions
112348
Defining the Complex numbers
40041
Proof of Non-Ordering of Complex Field
132525
Real Numbers Raised to Imaginary Powers?
113326
Proving orthogonality of vectors in a complex vector space