1.13 Complex numbers: polar and exponential formsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 1.13 Complex numbers: polar and exponential forms

1. The complex number $z=-1+\sqrt{3}\,i$.
   Write $z$ in the form $re^{i\theta}$, with $\theta$ in radians.2 marks
2. $z_1=3e^{\frac{\pi}{4}i}$ and $z_2=2e^{\frac{\pi}{12}i}$.
   Describe fully the single geometrical transformation of the Argand diagram that maps $z_1$ to $z_1z_2$.2 marks
3. The complex number $w=1+i$.
   Write $w$ in the form $re^{i\theta}$ and hence find $w^{10}$ in the form $a+bi$.3 marks