Question

Determine the modulus of each of the complex numbers in the matching pairs. List these moduli in order from smallest to largest. Use the letters of the matching pair in your listing.

A. -3 - i
B. 1 + i
C. 5 + 5i

Answer 1

To determine the modulus of complex numbers, use the formula Modulus = sqrt(Real part^2 + Imaginary part^2). The order of moduli from smallest to largest for the given complex numbers is B, A, C.

Step-by-step explanation:

To determine the modulus of a complex number, we use the formula:

Modulus = sqrt(Real part^2 + Imaginary part^2)

Let's calculate the modulus for each complex number:

A. Modulus of -3 - i = sqrt((-3)^2 + (-1)^2) = sqrt(10)

B. Modulus of 1 + i = sqrt((1)^2 + (1)^2) = sqrt(2)

C. Modulus of 5 + 5i = sqrt((5)^2 + (5)^2) = sqrt(50)

Now let's list the moduli in order from smallest to largest: B (sqrt(2)), A (sqrt(10)), C (sqrt(50)). Therefore, the correct order is BAC.