Complex number Calculator

What are Complex numbers?

An expression of the form \(a + bi\), where a and b are real values, is a complex number. For example, if z is a complex number and \(z = a + bi\), then a and b are the real and imaginary parts of z.

Numerous scientific disciplines, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory, require complex numbers.

How to Use the Complex Number Calculator?

The complex number calculator should be used as follows:

1. Fill in the appropriate input field with the complex numbers.
2. To obtain the outcome, press the “Calculate” button now.
3. Lastly, you will get two complex numbers’ multiplication, division, addition, or subtraction.

Basic operations with complex numbers

Working with complex numbers is simple because you may utilize the imaginary unit \(i\) as a variable. And to make complicated expressions simpler, use the formula \(i^2 = -1\). Numerous procedures are identical to those performed on two-dimensional vectors.

Addition

Combine the imaginary portions (with i) and the real parts (without i):

Use rule \((a + bi) + (c + di) = (a + c) + (b + d)i\) is equivalent to this.

\((1 + i) + (7 – 5i) = 8 – 4i\)

Subtraction

Subtract the imaginary components (with i) and the real parts again, very simply:

Use rule \((a + bi) + (c + di) = (a – c) + (b – d)i\) is equivalent to this.

\((10 – 5i) – (-6 + 5i) = 16 – 10i\)

Multiplication

You can use this formula for multiplication between two complex numbers, \(z_1\) and \(z_2\)

\(z_1 = a + bj\)

\(z_2 = c + dj\)

Multiplication Formula

\(= z_1 × z_2\)

\(= (a + bj) × (c + dj)\)

\(= ac + adj + bcj + bdj^2\)

But \(j^2 = -1\),

So \(z_1 × z_2 = (ac – bd) + (bc + ad)j\)

FAQs