(4+2i)(7+i)=

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Solution for (4+2i)(7+i)= equation:


Simplifying
(4 + 2i)(7 + i) = 0

Multiply (4 + 2i) * (7 + i)
(4(7 + i) + 2i * (7 + i)) = 0
((7 * 4 + i * 4) + 2i * (7 + i)) = 0
((28 + 4i) + 2i * (7 + i)) = 0
(28 + 4i + (7 * 2i + i * 2i)) = 0
(28 + 4i + (14i + 2i2)) = 0

Combine like terms: 4i + 14i = 18i
(28 + 18i + 2i2) = 0

Solving
28 + 18i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 9i + i2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2

Solution

i = {-7, -2}

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