(3+2i)(1-5i)=

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Solution for (3+2i)(1-5i)= equation:


Simplifying
(3 + 2i)(1 + -5i) = 0

Multiply (3 + 2i) * (1 + -5i)
(3(1 + -5i) + 2i * (1 + -5i)) = 0
((1 * 3 + -5i * 3) + 2i * (1 + -5i)) = 0
((3 + -15i) + 2i * (1 + -5i)) = 0
(3 + -15i + (1 * 2i + -5i * 2i)) = 0
(3 + -15i + (2i + -10i2)) = 0

Combine like terms: -15i + 2i = -13i
(3 + -13i + -10i2) = 0

Solving
3 + -13i + -10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -5i)(3 + 2i) = 0

Subproblem 1

Set the factor '(1 + -5i)' equal to zero and attempt to solve: Simplifying 1 + -5i = 0 Solving 1 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5i = 0 + -1 -5i = 0 + -1 Combine like terms: 0 + -1 = -1 -5i = -1 Divide each side by '-5'. i = 0.2 Simplifying i = 0.2

Subproblem 2

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

Solution

i = {0.2, -1.5}

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