IB Mathematics Applications & Interpretation Question Type 5: Performing Addition and Subtraction on Complex Numbers Exercises

Evaluate $(1-2i)-(-3+4i)-(2+i)$.

Compute the sum of the complex numbers $(-2+5i)$ and $(3-7i)$.

Find the midpoint of the line segment joining the points $-2+7i$ and $6-3i$ in the Argand plane.

Compute the sum of three complex numbers: $2+3i$, $-5+i$, and $4-7i$.

Calculate the difference $(7-2i)-(4+9i)$.

Given $z=2+5\text{i}$, the point representing $z$ on the Argand diagram is translated by the vector $\left(\genfrac{}{}{0ex}{}{-3}{-2}\right)$. Find the complex number representing the image and plot both points on an Argand diagram.

Compute the sum of the complex numbers $4+3i$ and $5-6i$.

A displacement of $5+2i$ is followed by one of $-3+6i$. Find the resultant displacement and plot both original displacements and the resultant on an Argand diagram.

Let points $A$ and $B$ represent the complex numbers $2+3i$ and $-1+i$ respectively. Given that $B-C=4-5i$, find the complex number $C$ and plot $A$, $B$, and $C$ on an Argand diagram.

Two force vectors are represented by complex numbers $6+2i$ and $-4+5i$. Determine the net force and represent it graphically on the Argand diagram.

The vertices of a triangle in the Argand plane are $z_1=1+2i$, $z_2=-3+i$, and $z_3$. Find $z_3$ so that the centroid of the triangle is at the origin. Then plot the triangle.