Question

Let the complex number z satisfy the equation

|z + 4i| = 3. Then the greatest and least values of |z + 3| are –

• A. 2, 8
• B. 2, 5
• C. 5, 8
• D. None of these

Answer 1

Answer: (A)

2, 8

Answer 2

Sol.

| z + 4i| = 3 ; PA £ |z – (– 3)| £ PB

5 – 3 £ |z + 3| £ 5 + 3 Ž 2 £ |z + 3| £ 8

PC = $\sqrt{3^{2} + 4^{2}}$ Ž PC = 5