Simplify the expression to a + bi form:

Question

left parenthesis, minus, 12, plus, 10, i, right parenthesis, minus, left parenthesis, minus, 8, plus, i, right parenthesis
(−12+10i)−(−8+i)

Answer 1

To simplify the expression \((-12 + 10i) - (-8 + i)\), follow these steps:

1. Distribute the negative sign in front of the second parentheses: \[ -12 + 10i + 8 - i \]

2. Combine the real parts and the imaginary parts:

   • Real parts: \(-12 + 8 = -4\)
   • Imaginary parts: \(10i - i = 9i\)

3. Write the final simplified expression in the form \(a + bi\): \[ -4 + 9i \]

Therefore, the simplified form of the expression is \(\boxed{-4 + 9i}\).