(4+i)(5-3i)=

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Solution for (4+i)(5-3i)= equation:


Simplifying
(4 + i)(5 + -3i) = 0

Multiply (4 + i) * (5 + -3i)
(4(5 + -3i) + i(5 + -3i)) = 0
((5 * 4 + -3i * 4) + i(5 + -3i)) = 0
((20 + -12i) + i(5 + -3i)) = 0
(20 + -12i + (5 * i + -3i * i)) = 0
(20 + -12i + (5i + -3i2)) = 0

Combine like terms: -12i + 5i = -7i
(20 + -7i + -3i2) = 0

Solving
20 + -7i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -3i)(4 + i) = 0

Subproblem 1

Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667

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 = {1.666666667, -4}

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