The modulus |z| of a complex number represents what geometric quantity?

Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

The modulus |z| of a complex number represents what geometric quantity?

The key idea is that the modulus measures length in the complex plane. If you write z as a + ib, the modulus is |z| = sqrt(a^2 + b^2). That value is exactly the Euclidean distance from the origin (0,0) to the point (a,b) representing z. So it tells you how far z is from the origin, not its real part, its imaginary part, or any difference between parts.

The key idea is that the modulus measures length in the complex plane. If you write z as a + ib, the modulus is |z| = sqrt(a^2 + b^2). That value is exactly the Euclidean distance from the origin (0,0) to the point (a,b) representing z. So it tells you how far z is from the origin, not its real part, its imaginary part, or any difference between parts.

More practice questions