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Further complex numbers — Question 153

Original QCE Vault practice · 1 mark

Q153 · Practice questionTechnology-freeComplex familiar1 mark

QUESTION 153

The points AA, BB and CC represent the three roots of z3=−8iz^3=-8i on the Argand plane. The point PP represents z=2z=2. What is the exact value of PA×PB×PCPA\times PB\times PC?
Equal-scale Argand plane: A=(sqrt(3),-1), B=(0,2), C=(-sqrt(3),-1), P=(2,0). Dashed segments join P to the three roots.
(A)
88
(B)
828\sqrt2
(C)
1616
(D)
128128
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