Complex Number Calculator

Use our free complex number calculator to explore all properties of a complex number or perform arithmetic operations between two complex numbers.

Math

Mode

z₁ =

z₂ =

Formula

Explore any complex number: view its real/imaginary parts, modulus, argument, conjugate, polar form, and trigonometric form. Or perform addition, subtraction, multiplication, and division of two complex numbers.

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

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter z₁ as a+bi (e.g., 3+4i, -2i, 5).
2For operations, also enter z₂.
3Select mode to view info or perform an operation.
4Click Calculate.

Examples

Info about 3+4i

1.|z| = 5, arg(z) = 53.13°
2.z̄ = 3−4i

Result: 5

Add 3+4i and 1+2i

1.(3+4i)+(1+2i) = 4+6i

Result: 7.2111025509

Frequently Asked Questions

A number of the form a+bi where a is real, b is imaginary, i = √(−1).

|z| = √(a²+b²) — the distance from the origin in the complex plane.

arg(z) = atan2(b,a) — the angle from the positive real axis.

Enter like 3+4i, -2i, 5, -1-i, 2.5-3.7i.

Yes, enter a number without i (e.g., 5 = 5+0i).

Related Calculators

Complex Addition Calculator Complex Multiplication Calculator Polar Form Calculator Euler Formula Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-15

Complex Number Calculator

Formula

How It Works

Examples

Info about 3+4i

Add 3+4i and 1+2i

Frequently Asked Questions

What is a complex number?

What is the modulus?

What is the argument?

What format should I use?

Can I enter just a real number?

Related Calculators

Complex Number Calculator

Formula

How It Works

Examples

Info about 3+4i

Add 3+4i and 1+2i

Frequently Asked Questions

What is a complex number?

What is the modulus?

What is the argument?

What format should I use?

Can I enter just a real number?

Related Calculators