(7+i)(6-8i)=

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Solution for (7+i)(6-8i)= equation:


Simplifying
(7 + i)(6 + -8i) = 0

Multiply (7 + i) * (6 + -8i)
(7(6 + -8i) + i(6 + -8i)) = 0
((6 * 7 + -8i * 7) + i(6 + -8i)) = 0
((42 + -56i) + i(6 + -8i)) = 0
(42 + -56i + (6 * i + -8i * i)) = 0
(42 + -56i + (6i + -8i2)) = 0

Combine like terms: -56i + 6i = -50i
(42 + -50i + -8i2) = 0

Solving
42 + -50i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -25i + -4i2) = 0

Factor a trinomial.
2((3 + -4i)(7 + i)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75

Subproblem 2

Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7

Solution

i = {0.75, -7}

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