(4+3i)(4-i)=0

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Solution for (4+3i)(4-i)=0 equation: 


Simplifying
(4 + 3i)(4 + -1i) = 0

Multiply (4 + 3i) * (4 + -1i)
(4(4 + -1i) + 3i * (4 + -1i)) = 0
((4 * 4 + -1i * 4) + 3i * (4 + -1i)) = 0
((16 + -4i) + 3i * (4 + -1i)) = 0
(16 + -4i + (4 * 3i + -1i * 3i)) = 0
(16 + -4i + (12i + -3i2)) = 0

Combine like terms: -4i + 12i = 8i
(16 + 8i + -3i2) = 0

Solving
16 + 8i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -1i)(4 + 3i) = 0


Subproblem 1
Set the factor '(4 + -1i)' equal to zero and attempt to solve:

Simplifying
4 + -1i = 0

Solving
4 + -1i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4

Subproblem 2
Set the factor '(4 + 3i)' equal to zero and attempt to solve:

Simplifying
4 + 3i = 0

Solving
4 + 3i = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3i = 0 + -4
3i = 0 + -4

Combine like terms: 0 + -4 = -4
3i = -4

Divide each side by '3'.
i = -1.333333333

Simplifying
i = -1.333333333
Solution
i = {4, -1.333333333}

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