Question

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

The moduli of the given complex numbers are calculated and ordered from smallest to largest as b (1.41), a (3.16), and c (7.07), resulting in the final answer: b, a, c.

Step-by-step explanation:

Ordering Complex Numbers by Magnitude

To list the given complex numbers a. -3 - i, b. 1 + i, and c. 5 + 5i in order from smallest to largest moduli, one must calculate the modulus (magnitude) of each complex number. The modulus of a complex number a + bi is √(a² + b²).

For a. -3 - i, the modulus is √((-3)² + (-1)²) = √(9 + 1) = √10 ≈ 3.16.

For b. 1 + i, the modulus is √(1² + 1²) = √(1 + 1) = √2 ≈ 1.41.

For c. 5 + 5i, the modulus is √(5² + 5²) = √(25 + 25) = √50 ≈ 7.07.

Ordering these from smallest to largest, we get:

• b. 1 + i (modulus ≈ 1.41)
• a. -3 - i (modulus ≈ 3.16)
• c. 5 + 5i (modulus ≈ 7.07)

Therefore, the correct option in final answer listing the moduli from smallest to largest is b, a, c.