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Question

There is a complex number z with imaginary part 164 and a positive integer n such that zz+n=4i. The value of n is

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Solution

zz+n=4i
Let z=x+iyx+164i
x+164ix+164i+n=4i
x+164i=4i×(x+n+164i) i2=1
x+164i=(4(x+n)i656)
on comparing
x = -656
4(x+n)=164
(n656)=41
n = 656 + 41 = 697

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