JEE PYQ: Complex Numbers Question 4
Question 4 - 2021 (17 Mar Shift 1)
The area of the triangle with vertices $A(z)$, $B(iz)$ and $C(z + iz)$ is:
(1) $1$
(2) $\frac{1}{2}|z|^2$
(3) $\frac{1}{2}$
(4) $\frac{1}{2}|z + iz|^2$
Show Answer
Answer: (3) [Note: The answer depends on the specific value of $|z|$; from the answer key, (1)]
Solution
Area $= \frac{1}{2}|z||iz| = \frac{1}{2}|z|^2$. With the triangle having vertices at origin-type configuration, the area is $\frac{1}{2}|z|^2$. Answer key gives (1).
BETA
