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Complex numbers 2 — Question 2

QCAA 2021, Paper 1 · 1 mark

Q2 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 2

When the polynomial

P(z)=z^3-iz^2-z-i

is divided by

z-i

, the remainder is

(A)

-2i

(B)

0

(C)

2i

(D)

4i

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

A

Worked solution

By the remainder theorem the remainder is

P(i)

. Since

i^2=-1

and

i^3=-i

,

P(i)=-i-i(-1)-i-i=-2i

.

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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