(7-3i)(2-i)=0

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Solution for (7-3i)(2-i)=0 equation: 


Simplifying
(7 + -3i)(2 + -1i) = 0

Multiply (7 + -3i) * (2 + -1i)
(7(2 + -1i) + -3i * (2 + -1i)) = 0
((2 * 7 + -1i * 7) + -3i * (2 + -1i)) = 0
((14 + -7i) + -3i * (2 + -1i)) = 0
(14 + -7i + (2 * -3i + -1i * -3i)) = 0
(14 + -7i + (-6i + 3i2)) = 0

Combine like terms: -7i + -6i = -13i
(14 + -13i + 3i2) = 0

Solving
14 + -13i + 3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -1i)(7 + -3i) = 0


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 '(7 + -3i)' equal to zero and attempt to solve:

Simplifying
7 + -3i = 0

Solving
7 + -3i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -3i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3i = 0 + -7
-3i = 0 + -7

Combine like terms: 0 + -7 = -7
-3i = -7

Divide each side by '-3'.
i = 2.333333333

Simplifying
i = 2.333333333
Solution
i = {2, 2.333333333}

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