IB Mathematics Analysis and Approaches Question Type 1: Drawing Complex Numbers on the Argand Diagram Exercises

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

Plot the points corresponding to $z=2+i$, $-z$, $\overline{z}$ and $-\overline{z}$ on an Argand diagram and describe the quadrilateral formed.

Given $z_1=2+3i$ and $z_2=-1+2i$, plot the point representing $z_1+z_2$ on an Argand diagram.

Let $z_1=1+\sqrt{3}i$. Find the image of $z_1$ under multiplication by $i$ and plot both points on an Argand diagram.

Plot the complex number $z=-3+4i$ and its reflection in the real axis on an Argand diagram.

Sketch the locus of points $z$ in the Argand diagram satisfying $$\mathrm{Re}(z)=-1$$

For $z=2+2i$, plot $z$ and $2z$ on the same Argand diagram.

Plot the complex number $z=1-i$ and its image under multiplication by $i$ on an Argand diagram.

The vertices of a triangle in the Argand diagram are given by: $$z_1=i,z_2=2,z_3=-1+2i$$

Plot these points and determine the coordinates of the centroid on the diagram.

Plot the complex number $z=1+2i$ and its conjugate $\overline{z}$ on an Argand diagram.