The locus $|z - a| = r$ on the Argand diagram is:

a circle, centre $a$, radius $r$

The locus $\arg(z - a) = \theta$ is:

a half-line from $a$ at angle $\theta$ (start point excluded)

12questions. Pick an answer and you'll see why right away.

The complex conjugate of $z = x + yi$ is:
To divide $\frac{z_1}{z_2}$ , you multiply numerator and denominator by:
If a real polynomial has $2 + 3i$ as a root, another root must be:
The modulus of $z = x + yi$ is:
Euler's relation states that $e^{i\theta}$ equals:
When two complex numbers are multiplied, the arguments:
De Moivre's theorem states that $(\cos\theta + i\sin\theta)^n$ equals:
To derive an identity for $\cos 3\theta$ from $(\cos\theta + i\sin\theta)^3$ , you take the:
With $z = \cos\theta + i\sin\theta$ , the expression $z + z^{-1}$ equals:
The $n$ th roots of a non-zero complex number are arranged on the Argand diagram as:
The locus $|z - a| = r$ on the Argand diagram is:
The locus $\arg(z - a) = \theta$ is: