(8+3i)(4+7i)=

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Solution for (8+3i)(4+7i)= equation:


Simplifying
(8 + 3i)(4 + 7i) = 0

Multiply (8 + 3i) * (4 + 7i)
(8(4 + 7i) + 3i * (4 + 7i)) = 0
((4 * 8 + 7i * 8) + 3i * (4 + 7i)) = 0
((32 + 56i) + 3i * (4 + 7i)) = 0
(32 + 56i + (4 * 3i + 7i * 3i)) = 0
(32 + 56i + (12i + 21i2)) = 0

Combine like terms: 56i + 12i = 68i
(32 + 68i + 21i2) = 0

Solving
32 + 68i + 21i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + 3i)(4 + 7i) = 0

Subproblem 1

Set the factor '(8 + 3i)' equal to zero and attempt to solve: Simplifying 8 + 3i = 0 Solving 8 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3i = 0 + -8 3i = 0 + -8 Combine like terms: 0 + -8 = -8 3i = -8 Divide each side by '3'. i = -2.666666667 Simplifying i = -2.666666667

Subproblem 2

Set the factor '(4 + 7i)' equal to zero and attempt to solve: Simplifying 4 + 7i = 0 Solving 4 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7i = 0 + -4 7i = 0 + -4 Combine like terms: 0 + -4 = -4 7i = -4 Divide each side by '7'. i = -0.5714285714 Simplifying i = -0.5714285714

Solution

i = {-2.666666667, -0.5714285714}

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