(-2+i)(-5-i)=

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Solution for (-2+i)(-5-i)= equation:


Simplifying
(-2 + i)(-5 + -1i) = 0

Multiply (-2 + i) * (-5 + -1i)
(-2(-5 + -1i) + i(-5 + -1i)) = 0
((-5 * -2 + -1i * -2) + i(-5 + -1i)) = 0
((10 + 2i) + i(-5 + -1i)) = 0
(10 + 2i + (-5 * i + -1i * i)) = 0
(10 + 2i + (-5i + -1i2)) = 0

Combine like terms: 2i + -5i = -3i
(10 + -3i + -1i2) = 0

Solving
10 + -3i + -1i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -1i)(5 + i) = 0

Subproblem 1

Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2

Subproblem 2

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

Solution

i = {2, -5}

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