(5+2j)*(3-2j)=

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Solution for (5+2j)*(3-2j)= equation:


Simplifying
(5 + 2j)(3 + -2j) = 0

Multiply (5 + 2j) * (3 + -2j)
(5(3 + -2j) + 2j * (3 + -2j)) = 0
((3 * 5 + -2j * 5) + 2j * (3 + -2j)) = 0
((15 + -10j) + 2j * (3 + -2j)) = 0
(15 + -10j + (3 * 2j + -2j * 2j)) = 0
(15 + -10j + (6j + -4j2)) = 0

Combine like terms: -10j + 6j = -4j
(15 + -4j + -4j2) = 0

Solving
15 + -4j + -4j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(3 + -2j)(5 + 2j) = 0

Subproblem 1

Set the factor '(3 + -2j)' equal to zero and attempt to solve: Simplifying 3 + -2j = 0 Solving 3 + -2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2j = 0 + -3 -2j = 0 + -3 Combine like terms: 0 + -3 = -3 -2j = -3 Divide each side by '-2'. j = 1.5 Simplifying j = 1.5

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 = {1.5, -2.5}

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