(2m-3n)i+(m+4n)=13+7i

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Solution for (2m-3n)i+(m+4n)=13+7i equation: 


Simplifying
(2m + -3n) * i + (m + 4n) = 13 + 7i

Reorder the terms for easier multiplication:
i(2m + -3n) + (m + 4n) = 13 + 7i
(2m * i + -3n * i) + (m + 4n) = 13 + 7i
(2im + -3in) + (m + 4n) = 13 + 7i

Remove parenthesis around (m + 4n)
2im + -3in + m + 4n = 13 + 7i

Solving
2im + -3in + m + 4n = 13 + 7i

Solving for variable 'i'.

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

Add '-7i' to each side of the equation.
2im + -3in + m + -7i + 4n = 13 + 7i + -7i

Reorder the terms:
-7i + 2im + -3in + m + 4n = 13 + 7i + -7i

Combine like terms: 7i + -7i = 0
-7i + 2im + -3in + m + 4n = 13 + 0
-7i + 2im + -3in + m + 4n = 13

Add '-1m' to each side of the equation.
-7i + 2im + -3in + m + -1m + 4n = 13 + -1m

Combine like terms: m + -1m = 0
-7i + 2im + -3in + 0 + 4n = 13 + -1m
-7i + 2im + -3in + 4n = 13 + -1m

Add '-4n' to each side of the equation.
-7i + 2im + -3in + 4n + -4n = 13 + -1m + -4n

Combine like terms: 4n + -4n = 0
-7i + 2im + -3in + 0 = 13 + -1m + -4n
-7i + 2im + -3in = 13 + -1m + -4n

Reorder the terms:
-13 + -7i + 2im + -3in + m + 4n = 13 + -1m + -4n + -13 + m + 4n

Reorder the terms:
-13 + -7i + 2im + -3in + m + 4n = 13 + -13 + -1m + m + -4n + 4n

Combine like terms: 13 + -13 = 0
-13 + -7i + 2im + -3in + m + 4n = 0 + -1m + m + -4n + 4n
-13 + -7i + 2im + -3in + m + 4n = -1m + m + -4n + 4n

Combine like terms: -1m + m = 0
-13 + -7i + 2im + -3in + m + 4n = 0 + -4n + 4n
-13 + -7i + 2im + -3in + m + 4n = -4n + 4n

Combine like terms: -4n + 4n = 0
-13 + -7i + 2im + -3in + m + 4n = 0

The solution to this equation could not be determined.

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