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If a complex number z, with integral real and imaginary parts, satisfies z2+ z̅2=16, then find the value of |z|.

If a complex number z, with integral real and imaginary parts, satisfies z2+ z̅2=16, then find the value of |z|. Correct Answer 101/2

Let z=x+iy, then, x2–y2=8 (by replacing z by x+iy in the given equation) Since, x and y are integers, |x|=3 and |y|=1 are the only possible values. Therefore, |z|=(32+12)1/2=101/2.

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