2016 Paper 1 Question 11

(a)

When $\lambda = 1$

$|z-i| = |z^*-i|$

Geometrically this means $z$ is as far from $i$ as $z^*$ .

Let $z = x +i\,y$

$\begin{aligned} |x+iy-i| &= |x-iy-i| \\ \Rightarrow x^2 + (y-1)^2 &= x^2 + (y+1)^2 \\ \Rightarrow y^2-2y+1 &= y^2 +2y +1 \\ \Rightarrow y &= 0 \end{aligned}$

$y=0$ is the equation of the straight line in the complex plane. This is consistent with the geometric interpretation.

(b)

When $\lambda = 0$ it must be that $z=i$ . This is another straight, horizontal, line.

NST First Year Maths

Some unofficial solutions to Cambridge NST IA maths papers

2016 Paper 1 Question 11

Leave a comment Cancel reply

Share this:

Related

Leave a comment Cancel reply