Question

the following statements concern the modulus. which statement is false? the modulus represents the distance between the complex number and the origin. the algorithm to find the modulus is based on the pythagorean theorem. the modulus is sometimes negative because of the computations with i. the modulus is an extension of the absolute value in the complex plane.

Explanation:

• The modulus of a complex number $z=a+bi$ is defined as $\sqrt{a^2 + b^2}$, which is a non-negative value (square root of a sum of squares can never be negative).
• It represents the distance from the complex number to the origin in the complex plane, so it is an extension of absolute value, and its calculation relies on the Pythagorean theorem.

Answer:

The modulus is sometimes negative because of the computations with $i$.