(4-j)(5+2j)=0

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Solution for (4-j)(5+2j)=0 equation:


Simplifying
(4 + -1j)(5 + 2j) = 0

Multiply (4 + -1j) * (5 + 2j)
(4(5 + 2j) + -1j * (5 + 2j)) = 0
((5 * 4 + 2j * 4) + -1j * (5 + 2j)) = 0
((20 + 8j) + -1j * (5 + 2j)) = 0
(20 + 8j + (5 * -1j + 2j * -1j)) = 0
(20 + 8j + (-5j + -2j2)) = 0

Combine like terms: 8j + -5j = 3j
(20 + 3j + -2j2) = 0

Solving
20 + 3j + -2j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(4 + -1j)(5 + 2j) = 0

Subproblem 1

Set the factor '(4 + -1j)' equal to zero and attempt to solve: Simplifying 4 + -1j = 0 Solving 4 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1j = 0 + -4 -1j = 0 + -4 Combine like terms: 0 + -4 = -4 -1j = -4 Divide each side by '-1'. j = 4 Simplifying j = 4

Subproblem 2

Set the factor '(5 + 2j)' equal to zero and attempt to solve: Simplifying 5 + 2j = 0 Solving 5 + 2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2j = 0 + -5 2j = 0 + -5 Combine like terms: 0 + -5 = -5 2j = -5 Divide each side by '2'. j = -2.5 Simplifying j = -2.5

Solution

j = {4, -2.5}

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