(4+i)(2-i)=

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


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

Multiply (4 + i) * (2 + -1i)
(4(2 + -1i) + i(2 + -1i)) = 0
((2 * 4 + -1i * 4) + i(2 + -1i)) = 0
((8 + -4i) + i(2 + -1i)) = 0
(8 + -4i + (2 * i + -1i * i)) = 0
(8 + -4i + (2i + -1i2)) = 0

Combine like terms: -4i + 2i = -2i
(8 + -2i + -1i2) = 0

Solving
8 + -2i + -1i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -1i)(4 + 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 '(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

Solution

i = {2, -4}

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