IB Maths AI HL AI 1.4 practice question

Paper 1Medium6 marks

The equation $x^2-8x+25=0$ has roots $z$ and $\bar z$ where $\operatorname{Im}(z)>0$

(a)

Find $z$ in Cartesian form.

[2]

(b)

Let

q=\frac{z-2}{\bar z-2}.

Find $q$ in Cartesian form.

[2]

(c)

Find the modulus and principal argument of $q$ Give the argument in radians, correct to three significant figures, in the range $-\pi<\arg(q)\leq\pi$

[2]