Question

A and B represent the complex numbers 1 + ai and 3 + bi and DOAB is an isosceles triangle right- angled at A. Then the values of a and b can be-

• A. a = 2, b = –1
• B. a = 1, b = –2
• C. a = 2, b = 1
• D. a = 2, b = –2

Answer 1

Answer: (C)

a = 2, b = 1

Answer 2

Sol. Since Š(OAB) = $\frac{\pi}{2}$and OA = AB,

(3 + bi) – (1 + ai) = (–1–ai)i

2 + (b –a)i = a –i

Comparison gives a = 2 and b = 1.

Another figure is also possible.

This gives a = –2 and b = –1.