Simplify (7-6i)(-8+3i)

Problem

(7−6*i)*(−8+3*i)

Solution

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

7*(−8)+7*(3*i)+(−6*i)*(−8)+(−6*i)*(3*i)

2. Perform the multiplication for each individual term.

−56+21*i+48*i−18*i2

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

−56+21*i+48*i−18*(−1)

4. Simplify the constant term resulting from the substitution.

−56+21*i+48*i+18

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

(−56+18)+(21*i+48*i)

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

−38+69*i

Final Answer

(7−6*i)*(−8+3*i)=−38+69*i

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