Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

(a)[3]

Solve the equation $iw^2=(2-2i)^2$ without using a calculator.

(b(i))[2]

Sketch an Argand diagram to show the region $R$, made up of the points representing the complex numbers $z$ for which $|z-4-4i|\leq 2$.

(b(ii))[6]

For the complex numbers shown by points in the region $R$, it is given that $p\leq|z|\leq q$ and $\alpha\leq\arg z\leq\beta$. Find the values of $p$, $q$, $\alpha$ and $\beta$, giving answers correct to 3 significant figures.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Expand and simplify to $iw^2=-8i$ or an equivalent form

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