Complex Numbers Practice
A-Level Complex Numbers — Interactive Practice
8 auto-graded practice problems covering Argand diagrams, modulus-argument form, De Moivre’s theorem, and roots of equations.
Argand Diagrams
easy
On an Argand diagram, the complex number z = 3 + 4i is plotted. What is its distance from the origin?
medium
If z = 2 − i, what is the complex number represented by the point obtained by rotating z by 90° anticlockwise about the origin?
Modulus-Argument Form
medium
Express z = 1 + √3 i in modulus-argument (r, θ) form.
easy
What is |z₁z₂| if |z₁| = 3 and |z₂| = 5?
De Moivre’s Theorem
hard
Using De Moivre\'s theorem, find (1 + i)⁶.
hard
Express cos(3θ) in terms of cos(θ) using De Moivre\'s theorem.
Roots of Equations
easy
Given that 2 + 3i is a root of a polynomial with real coefficients, what is another root?
medium
Find the modulus and argument of the 5th roots of unity on an Argand diagram.