(5m+4n)+(3m+6n)i=14+6i

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Solution for (5m+4n)+(3m+6n)i=14+6i equation:


Simplifying
(5m + 4n) + (3m + 6n) * i = 14 + 6i

Remove parenthesis around (5m + 4n)
5m + 4n + (3m + 6n) * i = 14 + 6i

Reorder the terms for easier multiplication:
5m + 4n + i(3m + 6n) = 14 + 6i
5m + 4n + (3m * i + 6n * i) = 14 + 6i
5m + 4n + (3im + 6in) = 14 + 6i

Reorder the terms:
3im + 6in + 5m + 4n = 14 + 6i

Solving
3im + 6in + 5m + 4n = 14 + 6i

Solving for variable 'i'.

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

Add '-6i' to each side of the equation.
3im + 6in + 5m + -6i + 4n = 14 + 6i + -6i

Reorder the terms:
-6i + 3im + 6in + 5m + 4n = 14 + 6i + -6i

Combine like terms: 6i + -6i = 0
-6i + 3im + 6in + 5m + 4n = 14 + 0
-6i + 3im + 6in + 5m + 4n = 14

Add '-5m' to each side of the equation.
-6i + 3im + 6in + 5m + -5m + 4n = 14 + -5m

Combine like terms: 5m + -5m = 0
-6i + 3im + 6in + 0 + 4n = 14 + -5m
-6i + 3im + 6in + 4n = 14 + -5m

Add '-4n' to each side of the equation.
-6i + 3im + 6in + 4n + -4n = 14 + -5m + -4n

Combine like terms: 4n + -4n = 0
-6i + 3im + 6in + 0 = 14 + -5m + -4n
-6i + 3im + 6in = 14 + -5m + -4n

Reorder the terms:
-14 + -6i + 3im + 6in + 5m + 4n = 14 + -5m + -4n + -14 + 5m + 4n

Reorder the terms:
-14 + -6i + 3im + 6in + 5m + 4n = 14 + -14 + -5m + 5m + -4n + 4n

Combine like terms: 14 + -14 = 0
-14 + -6i + 3im + 6in + 5m + 4n = 0 + -5m + 5m + -4n + 4n
-14 + -6i + 3im + 6in + 5m + 4n = -5m + 5m + -4n + 4n

Combine like terms: -5m + 5m = 0
-14 + -6i + 3im + 6in + 5m + 4n = 0 + -4n + 4n
-14 + -6i + 3im + 6in + 5m + 4n = -4n + 4n

Combine like terms: -4n + 4n = 0
-14 + -6i + 3im + 6in + 5m + 4n = 0

The solution to this equation could not be determined.

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