Complex Number Operations Calculator
Add, subtract, multiply and divide two complex numbers.
Enter your values
Enter the real part of z1 you are working with.
Enter the imaginary part of z1 you are working with.
Enter the real part of z2 you are working with.
Enter the imaginary part of z2 you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Sum
- 4 - 2i
- Difference
- 2 + 6i
- Product
- 11 - 10i
- Quotient
- -0.2941 + 0.8235i
Quick answer
Complex numbers combine like binomials, remembering that i^2 = -1, and division multiplies by the conjugate.
(a+bi)(c+di) = (ac-bd)+(ad+bc)i
At a glance
| What it does | Add, subtract, multiply and divide two complex numbers. |
|---|---|
| Category | Math |
| Inputs needed | Real part of z1, Imaginary part of z1, Real part of z2, Imaginary part of z2 |
| Main output | Sum |
| Formula | (a+bi)(c+di) = (ac-bd)+(ad+bc)i |
| Cost | Free — no sign-up, no download |
How to use the Complex Number Operations Calculator
- 1Enter the real and imaginary parts of both complex numbers.
- 2Sum, difference and product follow standard binomial expansion with i^2=-1.
- 3Division multiplies numerator and denominator by the conjugate of z2.
Inputs explained
- Real part of z1
- Enter the real part of z1 you are working with.
- Imaginary part of z1
- Enter the imaginary part of z1 you are working with.
- Real part of z2
- Enter the real part of z2 you are working with.
- Imaginary part of z2
- Enter the imaginary part of z2 you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Real part of z13
- Imaginary part of z12
- Real part of z21
- Imaginary part of z2-4
Results
- Sum4 - 2i
- Difference2 + 6i
- Product11 - 10i
- Quotient-0.2941 + 0.8235i
Frequently asked questions
What is i^2?
By definition, i^2 = -1.
What if z2 is zero?
Division is undefined when the denominator complex number is 0+0i.
What do I need to enter into the Complex Number Operations Calculator?
Just 4 values: real part of z1, imaginary part of z1, real part of z2, imaginary part of z2. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Complex Number Operations Calculator work out the answer?
Complex numbers combine like binomials, remembering that i^2 = -1, and division multiplies by the conjugate. It applies the formula (a+bi)(c+di) = (ac-bd)+(ad+bc)i and shows the working so you can check each step by hand.
Is the Complex Number Operations Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.