(i)[6]
Show that the modulus of z equals 2 \cos \theta and that the argument of z is \theta.
(ii)[3]
Prove that the real part of \frac{1}{z} stays constant.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The complex variable z is defined by z = 1 + \cos 2\theta + i \sin 2\theta, and \theta can take any value in the interval -\frac{1}{2}\pi < \theta < \frac{1}{2}\pi.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State a correct form for |z| or |z|^2, for example (1+\cos 2\theta)^2+(\sin 2\theta)^2” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI