Question 18 - A-Level Maths

Exam Board	Edexcel
Module	FP1 (Further Pure Mathematics 1)
Topic	Complex Numbers Arithmetic
Type	Standard quadratic with real coefficients

18. The complex number $z = a + \mathrm { i } b$, where $a$ and $b$ are real numbers, satisfies the equation $$z ^ { 2 } + 16 - 30 i = 0$$

Show that $a b = 15$.
Write down a second equation in $a$ and $b$ and hence find the roots of $$z ^ { 2 } + 16 - 30 i = 0$$