IB Mathematics Applications & Interpretation 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 $z_1{z}_2{z}_3$.

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.