A complex number consists of a real component and an imaginary component. The real component is an ordinary real number, the imaginary component is a real number with the letter i appened. The two components are combined with the addition (+) operator. In most cases you will have to put the complex number in parenthesis to make it clear that the number forms a unit.
Some valid complexes: 45+2i, 4.67+34e-23i
Constant | Definition |
---|---|
i | The imaginary unit |
Operator | Description | Examples |
---|---|---|
x + y | Addition | (1+2i)+(3+4i) |
x - y | Subtraction | (1+2i)-(3+4i) |
x * y | Complex multiplication or scalar multiplication depending on the types of x and y. The * sign can be omitted as with real numbers. | (1+2i)(3+4i), 3(1+2i) |
x / y | Division | (1+2i)/(3+4i) |
conj x | Conjugation | conj (1+2i) |
re x | Extracts the real component of x | re (5+3i) |
im x | Extracts the imaginary component of x | im (5+3i) |