Question

What is the magnitude of the complex number l−m if l=3+8i and m is a complex number?

(a) ∣l−m∣=3−8i
(b) ∣l−m∣=3+8i
(c) ∣l−m∣=√(3²+8²)
(d) ∣l−m∣=3−∣8i∣

Answer 1

The magnitude of the complex number l - m, with l = 3 + 8i, is correctly represented in general form by the expression |l - m| = √(3² + 8²), making

option (c) the correct answer.

Step-by-step explanation:

The magnitude of a complex number l - m, where l is known and m is any complex number, is calculated by subtracting m from l and then taking the modulus (absolute value) of the result. Since we are not given the exact value of m, we cannot calculate the specific magnitude of l - m. However, based on the given choices, we can determine the correct form for the magnitude of a complex number.

For a complex number z = a + bi, where a and b are real numbers, the magnitude is given by |z| = √(a² + b²). Therefore, for the complex number l = 3 + 8i, the theoretical magnitude if we were to subtract an unspecified complex number m would be a general formula similar to the square root of the sum of squares of the real part and the imaginary part of l.

Based on this, the correct answer that represents the magnitude of the complex number l - m in a general form is (c) |l - m| = √(3² + 8²). None of the other choices provide a correct representation of the magnitude of a complex number.