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Question

If (1+i1i)3(1i1+i)3=x+iy, find (x,y)


Solution

If (1+i1i)3(1i1+i)3=x+iy ((1+i)(1+i)(1i)(1+i))3((1i)(1i)(1+i)(1i))3=x+iy    [Rationalizing the denominator] (1+2i11+1)3(12i11+1)3=x+iy (2i2)3(2i2)3=x+iy i3(i)3=x+iy ii=x+iy 2i=x+iy

Comparing the real and imaginary parts,

(x, y) = (0, -2)

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