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;
- A complex number consists of a real and imaginary part.
- 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;
- Multiplication
- Division
- To divide complex numbers a numerical "trick" must be performed involving the denominator's complex conjugate.
- For example;
- Division
- 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