In mathematics, a variable that can take on the value of a complex number .
In basic algebra, the variables x and y generally stand for values of real numbers. The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + b i . The modulus of z is its absolute value . A complex variable may be graphed as a vector from the origin to the point (a,b) in a rectangular coordinate system , its modulus corresponding to the vector's length. Called an Argand diagram, this representation establishes a connection between complex analysis and vector analysis. See also Euler's formula .