Question

1. which expression is equivalent to the following:

(3 + 9i) - (5 - 3i)
options: -2 - 12i, -2 + 12i, 15 + 27i, 15 - 27i

Explanation:

Step1: Distribute the negative sign

$(3 + 9i) - 5 + 3i$

Step2: Combine real parts

$3 - 5 + 9i + 3i = -2 + 9i + 3i$

Step3: Combine imaginary parts

$-2 + (9 + 3)i = -2 + 12i$

Answer:

$-2 + 12i$ (the second option)