Complex Numbers
Add, multiply and divide complex numbers, and find the modulus, conjugate and polar form, with i² = −1 applied at each step. Try “(3 + 4i)(2 − i)”.
Try an example:
How the Complex Numbers works
- Expand like brackets, treating i as a variable.
- Replace i² with −1 and collect the real and imaginary parts.
- For division, multiply top and bottom by the conjugate of the denominator.
Frequently asked questions
What is the modulus of a complex number?
For a + bi it is √(a² + b²), the distance from the origin on the complex plane.
What is a complex conjugate?
The conjugate of a + bi is a − bi. A number times its conjugate is always real.
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