Question

Which subtraction expression has the difference 1 + 4i?

A) (-2 + 6i) - (1 - 2i)
B) (-2 + 6i) - (-1 - 2i)
C) (3 + 5i) - (2 - i)
D) (3 + 5i) - (2 + i)

Answer 1

Option D, which is (3 + 5i) - (2 + i), yields the correct difference of 1 + 4i when simplifying the subtraction expression between the complex numbers.

Step-by-step explanation:

To find which subtraction expression yields the difference of 1 + 4i, we can evaluate each option given:

• A) (-2 + 6i) - (1 - 2i) = -2 + 6i - 1 + 2i = -3 + 8i
• B) (-2 + 6i) - (-1 - 2i) = -2 + 6i + 1 + 2i = -1 + 8i
• C) (3 + 5i) - (2 - i) = 3 + 5i - 2 + i = 1 + 6i
• D) (3 + 5i) - (2 + i) = 3 + 5i - 2 - i = 1 + 4i

Option D gives us the correct difference of 1 + 4i, which is the answer we are looking for.