Question

The complex number satisfying arg (z + i) = $\frac{\pi}{4}$ and arg (2z + 3 –2i) = $\frac{3\pi}{4}$simultaneously, is –

• A. $\frac{1}{4}$– $\frac{3}{4}$I
• B. $\frac{1}{4}$+ $\frac{3}{4}$I
• C. –$\frac{1}{4}$– $\frac{3}{4}$I
• D. None

Answer 1

Answer: (D)

None

Answer 2

Sol. Let z = x + iy

arg (z + i) = $\frac{\pi}{4}$

Ž $\frac{y + 1}{x}$ = 1

Ž x = y + 1,

x > 0, y > – 1 ...(1)

arg (2z + 3 – 2i) = $\frac{3\pi}{4}$

Ž $\frac{2y - 2}{2x + 3}$ = – 1 Ž x + y = – $\frac{1}{2}$,

x < – $\frac{3}{2}$, y > 1 ... (2)

Hence (1) and (2) have no solution.