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Question

If z1 and z2 are two complex numbers such that z1 + z2 is a real number, then z2 = ____________.

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Solution

Given for two complex numbers, z1 and z2, we have z1+ z2 is real number
Let z1=x1+iy1 z2=x2+iy2z1+z2=x1+iy1+x2+iy2i.e z1+z2=x1+x2+iy1+y2Since z1+z2 is realy1+y2=0i.e y1=-y2i.e z2=x2+iy2 =x2-iy1

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