Complex Number Addition Calculator

Visualize and calculate the sum of two complex numbers in a fun and interactive way.

Complex Number 1 $$z_1 = a + bi$$

Real (a):

Imaginary (b):

Complex Number 2 $$z_2 = c + di$$

Real (c):

Imaginary (d):

Sum $$z_1 + z_2 = (a+c) + (b+d)i$$

Visual Representation

Understanding Complex Number Addition

Complex numbers are numbers that can be expressed in the form $$a + bi$$, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit (defined as $$i^2 = -1$$). 'a' is the real part, and 'b' is the imaginary part.

To add two complex numbers, say $$z_1 = a + bi$$ and $$z_2 = c + di$$, you simply add their real parts together and their imaginary parts together.

The formula for complex number addition is: $$z_1 + z_2 = (a + c) + (b + d)i$$

This calculator helps you perform this addition and visualize it on the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.