Question:medium

If a > 0, a R, z = a + 2i and |z| = -az + 1, then:

Show Hint

Modulus of a complex number is always real and non-negative.

Updated On: Mar 18, 2026

z is always a positive real number
z is always a negative real number
z is purely imaginary number
such a complex z does not exist

Show Solution

The Correct Option is D

Solution and Explanation

Was this answer helpful?

0

Top Questions on Complex numbers

Let $z$ be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34 \left| \frac{5z - 12}{5iz + 16} \right|^2$ is equal to :
- JEE Main - 2026
- Mathematics
- Complex numbers
View Solution
If \(x^2+x+1=0\), then the value of \(\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \dots + \left(x^{25} + \frac{1}{x^{25}}\right)^2\) is:
- JEE Main - 2026
- Mathematics
- Complex numbers
View Solution
Let \[ S = \{ z \in \mathbb{C} : 4z^2 + \bar{z} = 0 \}. \] Then \[ \sum_{z \in S} |z|^2 \] is equal to
- JEE Main - 2026
- Mathematics
- Complex numbers
View Solution
$z$ is a complex number satisfying \[ \left| \frac{z - 6i}{z - 2i} \right| = 1 \quad \text{and} \quad \left| \frac{z - 8 + 2i}{z + 2i} \right| = \frac{3}{5} \] then find $\sum |z|^2$.
- JEE Main - 2026
- Mathematics
- Complex numbers
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?

BITSAT - 2025
Vector Algebra

In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is \(c\), what is the velocity of sound in the gas?

BITSAT - 2025
kinetic theory

A ball is thrown vertically upward with a speed of 49 m/s. How long will it take to return to the thrower’s hand?

BITSAT - 2025
Kinematics

Two identical bodies of mass 1 kg each are moving towards each other with velocities of 5 m/s and 3 m/s, respectively. They collide elastically. What will be the velocity of the body initially moving at 5 m/s after the collision?

BITSAT - 2025
Mechanics