Secondary school › Complex numbers

Complex numbers: problems with solutions

41 groups of practice problems: the imaginary unit, operations, modulus, polar form, De Moivre's theorem, roots and rotations. Every problem has a step-by-step solution.

The problems are useful for the State Matura, for the external exam and for university entrance exams.

Topic	What you practise	Problems
The imaginary unit	Powers of i, real and imaginary parts, equal complex numbers, square roots and quadratic equations.	8
Operations and the conjugate	Conjugate, addition, multiplication, powers of 1 ± i, division and the inverse.	8
Modulus and the complex plane	Modulus, distance, equations with the modulus, lines and circles in the complex plane.	7
Polar coordinates	Polar coordinates, conversions, polar equations and polar curves.	4
Polar form and De Moivre's theorem	Polar form, arguments, multiplication and division in polar form and De Moivre's theorem.	7
Roots and rotations	n-th roots, equations, the locus Arg(z − z₀) = θ and rotations in the complex plane.	7