Question

The complex number which satisfy the equation

$z + \sqrt{2}|z + 1| + i = 0$is

• A. 2 + I
• B. – 2 + I
• C. – 2 – I
• D. 2 – i

Answer 1

Answer: (C)

– 2 – I

Answer 2

Sol. x + i(y + 1) +$\sqrt{2}$ |x + iy + 1| = 0

y + 1 = 0 Ž y = – 1 Q |x + i y + 1| is real

so $x + \sqrt{2}$ |x – i + 1| = 0

(x + 2)² = 0 Ž x = – 2