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Complex numbers 2 — Question 8

QCAA 2020, Paper 2 · 1 mark

Q8 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 8

Let

u=1+i

and

v=-12+5i

.

\operatorname{Re}(u^5-|v|)

is

(A)

-17

(B)

-4

(C)

8

(D)

9

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

A

Worked solution

(1+i)^2=2i

, so

(1+i)^4=-4

and

u^5=-4-4i

. Also

|v|=\sqrt{(-12)^2+5^2}=13

. Hence

u^5-|v|=-17-4i

, whose real part is

-17

.

Selects option A.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

View the full QCAA marking guide

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