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Further complex numbers — Question 173

Original QCE Vault practice · 5 marks

Q173 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 173 (5 marks)

Four beacons in a light installation have complex coordinates given by the solutions of (z−1−i)4=16(z-1-i)^4=16. They are represented on the Argand plane. The dashed circle has centre C=1+iC=1+i.
Four translated fourth roots on a radius-two circle centred at C=(1,1). Equal scales.
a)
Determine all four solutions in Cartesian form.
[3 marks]
b)
Determine the greatest distance from the origin and every solution attaining it.
[2 marks]
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