GATE CH 2023 | Question: 13

Question

Given that

$$F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$$

where $z_1=2+3 i$ and $z_2=-2+3 i$ with $i=\sqrt{-1}$, which one of the following options is $\text{CORRECT}$?

• A. $F<0$
• B. $F<1$
• C. $F>1$
• D. $F=1$

Answer 1

F=|Z_1+Z_2 |/(|Z_1 |+|Z_2 | )

Z1 = 2+3i Z2 = -2+3i

F=  |6i|/(√13+√13) = √36/(2√13) = 0.83 < 1

Therefore, F < 1