Simplify (8+4i)(6-8i)

Problem

(8+4*i)*(6−8*i)

Solution

1. Apply the FOIL method to multiply the two binomials by distributing each term in the first set of parentheses to each term in the second.

8*(6)+8*(−8*i)+4*i(6)+4*i*(−8*i)

2. Multiply the terms to find the individual products.

48−64*i+24*i−32*i2

3. Substitute the identity i2=−1 into the expression.

48−64*i+24*i−32*(−1)

4. Simplify the constant by performing the multiplication.

48−64*i+24*i+32

5. Combine like terms by adding the real parts together and the imaginary parts together.

(48+32)+(−64*i+24*i)

6. Calculate the final sums to reach the simplified form.

80−40*i

Final Answer

(8+4*i)*(6−8*i)=80−40*i

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