Dive into Complex Numbers

Perform complex number arithmetic with ease and visualize the results instantly.

Enter real and imaginary parts, choose an operation, and explore!

Enter Complex Numbers

First Complex Number (z1):

Real Part (a):

Imaginary Part (b): i

Second Complex Number (z2):

Real Part (c):

Imaginary Part (d): i

Choose Operation

Result

Understanding Complex Numbers

Complex numbers are numbers of the form $$a + bi$$ , where $$a$$ and $$b$$ are real numbers, and $$i$$ is the imaginary unit with the property $$i^2 = -1$$ .

Basic Operations:

Addition: $$(a + bi) + (c + di) = (a+c) + (b+d)i$$
Subtraction: $$(a + bi) - (c + di) = (a-c) + (b-d)i$$
Multiplication: $(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i$
Division: $\frac{a + bi}{c + di} = \frac{ac + bd}{c^2 + d^2} + \frac{bc - ad}{c^2 + d^2}i$

Use this interactive tool to perform these operations and deepen your understanding of complex numbers. Explore further resources online or in textbooks to learn more about complex number theory and applications.

Learn more about complex numbers on Wikipedia or Khan Academy.