Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

(a)[5]

Without using a calculator and showing all your working, determine the square roots of the complex number $7 - 6\sqrt{2}i$. Present your answers in the form $x + iy$, where $x$ and $y$ are real and exact.

(b(i))[4]

On an Argand diagram, draw the loci corresponding to complex numbers $w$ and $z$ that satisfy $|w - 1 - 2i| = 1$ and $\arg(z - 1) = \frac{3}{4}\pi$.

(b(ii))[2]

Calculate the least value of $|w - z|$ for points on these loci.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: After squaring $x+iy$, set the real part equal to $7$ and the imaginary part equal to $-6\sqrt{2}$ respectively

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