Imaginary Number Calculator

Find the modulus, conjugate and argument of a + bi.

Modulus |z| 5

Argument (°) 53.13

Conjugate imaginary part (i) -4

Formula: |z| = √(a² + b²), arg = atan2(b, a)

Step-by-step with your numbers:

1. Values used:

2. Real part a = 3

3. Imaginary part b = 4 i

5. Modulus |z| = 5

6. Argument = 53.13°

7. Conjugate imaginary part = -4i

Did we solve your problem today?

Explore a complex (imaginary) number a + bi: its size, direction and conjugate.

The math behind it

The modulus |z| = √(a² + b²) is its distance from the origin. The argument is its angle. The conjugate flips the sign of the imaginary part.

3 + 4i → modulus 5, argument ≈ 53.13°, conjugate 3 − 4i.

What is the imaginary unit?

i, defined by i² = −1.