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Further complex numbers — Question 148

Original QCE Vault practice · 1 mark

Q148 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 148

The four roots of z4=−16z^4=-16 are shown on the Argand plane. For each root, a new complex number is defined by
w=z+4z.w=z+\frac{4}{z}.
Which statement describes the set of distinct values of ww?
Argand diagram with four roots of z to the fourth equals minus sixteen, lying on a radius-two circle.
(A)
Only the origin.
(B)
Exactly two points on the imaginary axis.
(C)
Exactly two points on the real axis.
(D)
Four points on a circle of radius 4 centred at the origin.
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