(6-3i)(2-i)=

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Solution for (6-3i)(2-i)= equation:


Simplifying
(6 + -3i)(2 + -1i) = 0

Multiply (6 + -3i) * (2 + -1i)
(6(2 + -1i) + -3i * (2 + -1i)) = 0
((2 * 6 + -1i * 6) + -3i * (2 + -1i)) = 0
((12 + -6i) + -3i * (2 + -1i)) = 0
(12 + -6i + (2 * -3i + -1i * -3i)) = 0
(12 + -6i + (-6i + 3i2)) = 0

Combine like terms: -6i + -6i = -12i
(12 + -12i + 3i2) = 0

Solving
12 + -12i + 3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4i + i2) = 0

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

Ignore the factor 3.

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 '(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

Solution

i = {2, 2}

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