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 `ai*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

Quiz on complex numbers (complex numbers): This quiz allows you to apply algebraic calculation techniques to complex numbers.
Complex numbers : exercises
 Exercise 1701, algebraic form of a complex number  complex numbers : The goal of this corrected exercise is to write a complex number in its algebraic form z=a+ib.
 Exercise 1702, real part of a complex number  complex numbers : To succeed in this exercise, you must know how to determine the real part of a complex expression.
 Exercise 1703, imaginary part of a complex number  complex numbers : The purpose of this exercise is to determine with the help of calculation, the imaginary part of a complex number.
 Exercise 1704, calculate the conjugate of a complex number  complex numbers : This exercise allows to implement the techniques of calculation of the conjugate of a complex number.
 Exercise 1705, operations on complex numbers  complex numbers : The purpose of this exercise is to find the result of arithmetic operations (sum, difference, product) that involve complex numbers.
 Exercise 1706, imaginary part of a complex number  complex numbers : The objective of this exercise is to find the imaginary part of a complex number from its algebraic form.
 Exercise 1707, real part of a complex number  complex numbers : The objective of this exercise is to find the real part of a complex number from its algebraic form.
 Exercise 1708, affix of a complex number  complex numbers : The purpose of this graphing exercise is to place in the plane the affix of a complex number.
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