Do not use a calculator in answering this question. Find the roots of the equation \(x^2(1+\mathrm{i

Question

Do not use a calculator in answering this question. Find the roots of the equation $x^2(1+\mathrm{i})-4x+(4-4\mathrm{i})=0$, giving your answers in cartesian form $a+\mathrm{i}b$.[3] The complex numbers $z$ and $w$ are such that $z=1+\mathrm{i}$ and $w=-1-\mathrm{i}\sqrt{3}$. Find the modulus and argument of $\frac{z}{w^*}$ exactly.[3]

Accepted Answer

(ii) $- \tan ^{-1} \left( 2+\sqrt{3} \right) $

Complex Numbers

Complex Numbers