A selection of free mathematical resources (calculators, exercises, games, quizzes, course reminders) to learn how to calculate 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`.

Second degree equation with real coefficients

Complex numbers : calculators

Complex numbers : games and quizzes

  • This quiz allows you to apply algebraic calculation techniques to complex numbers. Quiz on complex numbers (complex numbers): This quiz allows you to apply algebraic calculation techniques to complex numbers.

Complex numbers : exercises

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