Write the result of multiplication of (7-5i)(-7+8i).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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