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

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


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

Multiply (3 + 7i) * (4 + i)
(3(4 + i) + 7i * (4 + i)) = 0
((4 * 3 + i * 3) + 7i * (4 + i)) = 0
((12 + 3i) + 7i * (4 + i)) = 0
(12 + 3i + (4 * 7i + i * 7i)) = 0
(12 + 3i + (28i + 7i2)) = 0

Combine like terms: 3i + 28i = 31i
(12 + 31i + 7i2) = 0

Solving
12 + 31i + 7i2 = 0

Solving for variable 'i'.

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

Subproblem 1

Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 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 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4

Subproblem 2

Set the factor '(3 + 7i)' equal to zero and attempt to solve: Simplifying 3 + 7i = 0 Solving 3 + 7i = 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 + 7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7i = 0 + -3 7i = 0 + -3 Combine like terms: 0 + -3 = -3 7i = -3 Divide each side by '7'. i = -0.4285714286 Simplifying i = -0.4285714286

Solution

i = {-4, -0.4285714286}

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