Simplify the expression to a + bi form:

Question

left parenthesis, minus, 9, plus, 5, i, right parenthesis, left parenthesis, minus, 5, minus, 7, i, right parenthesis
(−9+5i)(−5−7i)

Answer 1

To simplify the expression \((−9 + 5i)(−5 − 7i)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms: \[ (-9)(-5) = 45 \]

2. Multiply the outer terms: \[ (-9)(-7i) = 63i \]

3. Multiply the inner terms: \[ (5i)(-5) = -25i \]

4. Multiply the last terms: \[ (5i)(-7i) = -35i^2 \]

   Since \(i^2 = -1\), we can replace \(-35i^2\) with \(35\): \[ -35i^2 = -35(-1) = 35 \]

Now, combine all the results: \[ 45 + 63i - 25i + 35 \]

Combine the real parts (45 and 35) and the imaginary parts (63i and -25i): \[ (45 + 35) + (63i - 25i) = 80 + 38i \]

So, the expression simplified to \(a + bi\) form is: \[ \boxed{80 + 38i} \]