Question

The complex number which satisfies 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. Let z = x + iy Ž x + iy +$\sqrt{2}$| (x + 1) + iy| + i = 0

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

x +$\sqrt{2}$ ($\sqrt{(x + 1)^{2} + y^{2}}$) +i(y + 1) = 0 + i0

Comparing y = – 1, x = – 2 so, z = – 2 – i