A. A real number
B. An imaginary number
C. Both are real numbers
D. Both are imaginary numbers
Answer & Solution
Let $Z$ = x + iy and $\overline{Z}$ = x - iy
∴ $Z+\overline{Z}$
= (x + iy) + (x - iy)
= 2x [which is real a number.]
∴ $Z\overline{Z}$ = (x + iy) ⚹ (x - iy)
= x2 - i2 ⚹ y2 [ ∵ i2 = -1]
= x2 + y2 [which is a real number.]