Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

The complex numbers $v$ and $w$ are defined by the equations $v + iw = 5$ and $(1 + 2i)v - w = 3i$.
(a)[6]

Solve the equations for $v$ and $w$, and write each answer in the form $x + iy$, with $x$ and $y$ real.

(b(i))[2]

On an Argand diagram, sketch the locus of points for complex numbers $z$ that satisfy $|z - 2 - 3i| = 1$.

(b(ii))[2]

Calculate the smallest value of $\arg z$ for points on this locus.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Solve and determine $v$ or $w$.

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