Complex Numbers Questions and Answers

The complex number $u = \dfrac{1}{-2+i}$. Find $|u|$.

Given $w = 1 + 2i$ and $u = 3 - i$, express $uw$ in the form $a + ib$.

The equation $x^3 - 2x^2 + 4x - 8 = 0$ has a root $x = 2i$. Find the other two roots.

The complex number $u=\dfrac{5+4i}{3-2i}$. Express $u$ in the form $x+iy$.

For $u=\dfrac7{13}+\dfrac{22}{13}i$, find the modulus $|u|$.

For $u=\dfrac7{13}+\dfrac{22}{13}i$, find the argument of $u$ in degrees.

The complex number $u\approx0.54+1.69i$. What does the locus $|z-u|=2$ represent on an Argand diagram?