IB Mathematics Analysis and Approaches Question Type 2: Finding the Roots of Complex Numbers Exercises

Find all complex solutions of $z^2=5+12i$ and express them in the form $a+bi$.

Find all complex solutions of $z^4=-8i$ and express them in polar form.

Find all complex solutions of $z^6=-64$ and express them in the form $a+bi$.

Solve $z^6=(4+4\sqrt{3}i{)}^3$ and express all six solutions in the form $a+bi$.

Find all complex solutions of $z^8=-1$ and plot them on the Argand diagram.

Solve $z^7=-128i$ and express all solutions in polar form.

Find all complex solutions of $z^6=64$ and express them in polar form.

Solve $z^4=16+16i$ and express all roots in polar form.

Find all complex solutions of $z^2=9$ and plot them on the Argand diagram.

Solve $z^5=32(\cos 45^{\circ }+i\sin 45^{\circ })$ and express all roots in the form $a+bi$.

Find all complex solutions of $z^3=4+3i$ and plot them on the Argand diagram.

Find all complex solutions of $w^3=(1+i\sqrt{3}{)}^5$ and express them in the form $a+bi$.

Determine all complex solutions of $z^4=16(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3})$ and plot them on the Argand diagram.