Question

f(z) is a complex valued function f(z)= (a + ib) z where a, b Ī R and |a+ ib| = $\frac{1}{\sqrt{2}}$. It has the property that f(z) is always equidistant from 0 and z, then a –b =

• A. 0
• B. 5
• C. 6
• D. 25

Answer 1

Answer: (A)

0

Answer 2

Sol. |a + ib| |z| = |z| |(a –1) + ib|

Ž $\frac{1}{\sqrt{2}}$= $\sqrt{(a - 1)^{2} + b^{2}}$and a² + b² = $\frac{1}{2}$

Ž 1 –2a = 0 Ž a = $\frac{1}{2}$

and b² = $\frac{1}{4}$ Ž b =$\frac{1}{2}$ Ž a – b = 0