2023TrialMultiple choice

Q2

1 mark

Question

In which quadrant is the complex number $(-3+3i)^3$ located on the Argand plane?

(A) The first quadrant

(B) The second quadrant

(D) The fourth quadrant

Try the question before revealing the answer.

Solution

Answer: A

(-3+3i)^3=(-3)^3+3(-3)^2(3i)+3(-3)(3i)^2+(3i)^3

=-27+81i-81i^2+27i^3

=-27+81i+81-27i

=54+54i

$(A)$

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Syllabus alignment

Complex Numbers

Arithmetic of complex numbersRepresent and calculate with complex numbers in Cartesian form, including conjugates, division, reciprocals and square roots.
Geometric representation of a complex numberRepresent complex numbers in the complex plane and use modulus, argument and polar form with their identities.

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