Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

For the complex numbers $u = a + ib$ and $w = c + id$, with $a$, $b$, $c$ and $d$ all real.
(a)[2]

Prove $(u + w)^* = u^* + w^*$.

(b)[4]

Solve the equation $(z + 2 + i)^* + (2 + i)z = 0$, and give the answer in the form $x + iy$ where $x$ and $y$ are real.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $u$ and $w$ and give the correct conjugate.” …

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