To multiply (7-5i)(-7+8i),
First open the brackets and multiply all the terms with each other. Then simplify by adding the real and complex terms together.
=> 7*-7 + 7*8i + 7*5i - 40i^2
=> -49 + 56i + 35i + 40
=> -9 + 91i
Therefore we get (7-5i)(-7+8i) = -9 + 91i
We'll use the property of distributivity of multiplication over the addition.
We'll remove the brackets:
(7-5i)(-7+8i) = 7*(-7+8i) - 5i(-7+8i)
We'll remove the brackets from the right side:
(7-5i)(-7+8i) = -49 + 56i + 35i - 40i^2
We'll keep in mind that i^2 = -1 and we'll substitute in the expression above.
(7-5i)(-7+8i) = -49 + 91i + 40
We'll combine real terms:
(7-5i)(-7+8i) = -9 + 91i