Question

If 0 $\le$ Argz $\le \frac{\pi }{4}$, then the least value of $\sqrt{2}$ |2z - 4i| is

• A. 6
• B. 1
• C. 4
• D. 2

Answer 1

The correct option is C

4

0 $\le$ Argz $\le \frac{\pi }{4}$, represents the region of complex plane lying in the first quadrant and bounded by x-axis and the line y = x

|2z - 4i| = 2|z - 2i|

least value of |z - 2i| is length of perpendicular from (0,-2): to y = x, which is $\sqrt{2}$

So the least value of $\sqrt{2}$ |2x - 4i| is 4