Question Type 1: Plotting complex numbers on an Argand diagram Exercises

Given $z_1 = 2 + 3i$ and $z_2 = -1 + i$, plot both points on an Argand diagram and calculate the distance between them.

Given $z = 2 + i$, find the value of $w = (1 + i)z$. Plot both $z$ and $w$ on an Argand diagram, and describe the transformation effected by multiplication by $1 + i$.

Plot the complex number $z = 3 + 4i$ on an Argand diagram.

Given $z_1 = 3 - 2i$ and $z_2 = -1 + 4i$, find the midpoint of the segment joining them and plot $z_1$, $z_2$, and the midpoint on an Argand diagram.

Let $z = 2 - 2i$. Find and plot $w = iz$ on an Argand diagram, and describe the geometric transformation mapping $z$ to $w$.

Sketch the locus of points $z$ satisfying $|z - (1 - 2i)| = 3$; indicate the centre and radius on your sketch.

Let $z = 2 + 3i$. Plot $z$ and its complex conjugate $\overline{z}$ on an Argand diagram.

Given $z_1 = 1 + i$, $z_2 = 1 + 3i$, $z_3 = 3 + 3i$, and $z_4 = 3 + i$, plot these points on an Argand diagram and prove they are the vertices of a square.

Plot the points corresponding to $z_1 = 1 + i$, $z_2 = 4 + i$, and $z_3 = 1 + 4i$ on an Argand diagram and calculate the area of triangle $z_1z_2z_3$.

Given $z_1 = 1 + 2i$ and $z_2 = 3 - 4i$, plot $z_1$, $z_2$, and $z_1 + z_2$ on an Argand diagram, and explain how this illustrates vector addition.

Plot the complex number $z = -2 - 5i$ on an Argand diagram.

Plot the complex number $z = 5e^{i\frac{\pi}{4}}$ on an Argand diagram by converting it to Cartesian form first.