# Complex Numbers

- The theory of complex numbers was developed by Jean le Rond d′Alembert in 1746. The vector representation of complex numbers was introduced by Casper Wessel in 1798.

- A complex number consists of a real and imaginary part.
- For example, if;
- where
*a*and*b*are real numbers and*i*is imaginary. The real part of*z*, denoted Re*z*or re*z*, is*a*. The imaginary part of*z*, denoted Im*z*or im*z*, is*b*.

**Addition & Subtraction**- To add and subtract complex numbers the real and imaginary parts are treated as separate entities.
- For example;

**Multiplication**- To multiply complex numbers, both terms in the first complex number are multiplied by both terms in the second complex number.
- For example;

**Division**- To divide complex numbers a numerical "trick" must be performed involving the denominator's complex conjugate.
- For example;
- Two complex numbers are said to be equal when their real parts are equal and when their imaginary parts are equal.

**Modulus or Magnitude**

**Argument**

**See also: **Complex Conjugate, Complex Numbers, Exponential Form, Complex Numbers, Logarithms of, Complex Numbers, Polar Form, Conjugation, de Moivre, Imaginary Axis, Imaginary Number, Imaginary Part, Real Part.

**Subjects: ** Mathematics