Two nonzero complex numbers such that $| z_1 + z_2 |$ = $| z_1 - z_2 |$. If $z_2 ≠ 0$, show that $\frac{z_1}{z_2}$ is a pure imaginary.
13794
$|z_{1} + z_{2}| = |z_{1} - z_{2}| \implies z_{1}/z_{2}$ is Imaginary
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
40824
Complex Equation Of a Circle $|z-z_1|^2+|z-z_2|^2=k$.
149529
Name for complex number with nonzero imaginary component
106197
Complex numbers - Exponential numbers - Proof
71566
Positive and negative complex numbers?
140968
Proof for Property of Complex Numbers
124037
Complex prime numbers
42165
Complex numbers and Roots of unity
5032
Compute $e^{e^z}$, where z is a complex number
148223
If the complex number Z satisfies $ |Z^2 - 9| + |Z^2| = 41 $ then the true statements among the following are?
101491
If $\frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|}$, then why is $\frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}=0$?
70974
How can zero divided by $i$ be $2\pi$?
90549
If $z^2 = z_1^2+z_2^2+z_3^2$ then $|\Re(z)| \le|\Re(z_1)|+|\Re(z_2)|+|\Re(z_3)|$
94962
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right)  = 0$
142076
$c$ is a complex number that satisyfing $(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$
24221
Complex numbers - minimum value proof