(3+I)(5+I)=

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Solution for (3+I)(5+I)= equation:


Simplifying
(3 + I)(5 + I) = 0

Multiply (3 + I) * (5 + I)
(3(5 + I) + I(5 + I)) = 0
((5 * 3 + I * 3) + I(5 + I)) = 0
((15 + 3I) + I(5 + I)) = 0
(15 + 3I + (5 * I + I * I)) = 0
(15 + 3I + (5I + I2)) = 0

Combine like terms: 3I + 5I = 8I
(15 + 8I + I2) = 0

Solving
15 + 8I + I2 = 0

Solving for variable 'I'.

Factor a trinomial.
(5 + I)(3 + I) = 0

Subproblem 1

Set the factor '(5 + I)' equal to zero and attempt to solve: Simplifying 5 + I = 0 Solving 5 + I = 0 Move all terms containing I to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + I = 0 + -5 Combine like terms: 5 + -5 = 0 0 + I = 0 + -5 I = 0 + -5 Combine like terms: 0 + -5 = -5 I = -5 Simplifying I = -5

Subproblem 2

Set the factor '(3 + I)' equal to zero and attempt to solve: Simplifying 3 + I = 0 Solving 3 + I = 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 + I = 0 + -3 Combine like terms: 3 + -3 = 0 0 + I = 0 + -3 I = 0 + -3 Combine like terms: 0 + -3 = -3 I = -3 Simplifying I = -3

Solution

I = {-5, -3}

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