A complex number is an ordered pair of two real numbers (a,b). To represent a complex number, we can use the algebraic notation, z=a+ib with i^2=-1. These numerous mathematical resources (calculators, quizzes, games, exercises, course reminders) allow you to practice calculating with complex numbers.

## Complex numbers : Reminder

A complex number is an ordered pair of two real numbers (a, b).

To represent a complex number, we use the algebraic notation or algebraic form, z = a + ib with i^2=-1

### Conjugate of a complex number

The conjugate of a complex number a+i*b , where a and b are reals, is the complex number a-i*b.

### Modulus of a complex number

The modulus of a complex number z=a+ib (where a and b are real) is the positive real number, denoted |z| , defined by : |z|=sqrt(a^2+b^2).

### Amplitude of a complex number

The plan has a direct orthogonal reference (O,vec(i),vec(j)). Lets z a non zero complex number and M its image. Called the amplitude of the complex number z, any measure, expressed in radians, of the angle (vec(i),vec(OM)).

### Trigonometric form of a complex number

A complex number z of argument theta and modulus r, can be written in its trigonometric form z=r(cos(theta)+i*sin(theta)), |z| = r, arg(z) = theta.

### Exponential notation of a complex number

For any real theta, we note e^(i*theta) the complex number cos(theta)+i*sin(theta).

A complex number z of amplitude theta and modulus r, can be written in its exponential form z=r*e^(i*theta), |z| = r, arg(z) = theta.