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Let a, b, and c be complex numbers. Let a1 be the image of a when it is rotated 90 degrees clockwise around b. Let a2 be the image of a1 when it is rotated 90 degrees counter-clockwise around c.



Then a2 can be written in the form a2=pa+qb+rc
for some complex numbers p ,q , and r. Find p^2+q^2+r^2.

 

Thanks everyone! This problem is soooo hard for me :(

BasicMaths
 

 Jan 24, 2020
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p = i, q = 1 + i, and r = -1 - i, so p^2 + q^2 + r^2 = 4i - 1.

 Jan 24, 2020

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