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

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

• A. Imaginary axis value
• B. Difference between parts
• C. Distance from origin to that number
• D. Real part

Answer: (C)

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.