JEE PYQ: Complex Numbers Question 41
Question 41 - 2019 (11 Jan Shift 2)
Let $z$ be a complex number such that $|z| + z = 3 + i$ (where $i = \sqrt{-1}$). Then $|z|$ is equal to:
(1) $\frac{\sqrt{34}}{3}$
(2) $\frac{5}{3}$
(3) $\frac{\sqrt{41}}{4}$
(4) $\frac{5}{4}$
Show Answer
Answer: (2)
Solution
$|z| + z = 3 + i$. Let $z = a + i$: then $|z| = 3 - a$. $\sqrt{a^2+1} = 3-a \Rightarrow a^2+1 = 9-6a+a^2 \Rightarrow a = \frac{4}{3}$. $|z| = 3 - \frac{4}{3} = \frac{5}{3}$.
BETA
