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Further complex numbers — Question 183

Original QCE Vault practice · 5 marks

Q183 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 183 (5 marks)

Four corners of a square game arena have complex coordinates satisfying z4=−81z^4=-81. The dashed circle is centred at the origin.
Four roots of z to the fourth equals minus 81 on a radius-three circle. Equal scales.
a)
Determine all four roots in polar form.
[3 marks]
b)
Determine the side length and area of the square exactly.
[2 marks]
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