What is the answer to (x/((3+4i)))+(((2x+5i))/((1-2i)))=2+2i ?

The answer to (x/((3+4i)))+(((2x+5i))/((1-2i)))=2+2i is x=4-3i

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(x/((3+4i)))+(((2x+5i))/((1-2i)))=2+2i

(\frac{x}{( 3 + 4 i )}) + (\frac{( 2 x + 5 i )}{( 1 - 2 i )}) = 2 + 2 i

x = 4 - 3 i

Solution steps

(\frac{x}{( 3 + 4 i )}) + (\frac{( 2 x + 5 i )}{( 1 - 2 i )}) = 2 + 2 i

Expand

(\frac{x}{3 + 4 i}) + (\frac{2 x + 5 i}{1 - 2 i}) : \frac{13 x}{25} - 2 + \frac{16 i x + 25 i}{25}

\frac{13 x}{25} - 2 + \frac{16 i x + 25 i}{25} = 2 + 2 i

Multiply both sides by

25

13 x - 50 + 16 i x + 25 i = 50 + 50 i

Move

25 i

to the right side

13 x - 50 + 16 i x = 50 + 25 i

Move

50

to the right side

13 x + 16 i x = 100 + 25 i

Factor

13 x + 16 i x : (13 + 16 i) x

(13 + 16 i) x = 100 + 25 i

Divide both sides by

13 + 16 i

x = 4 - 3 i

- 9 x - 6 = - 15.5 x + 46

(2 - 2) = (6 y)

\frac{( 2 z )}{( 1 + i )} - \frac{( 2 z )}{i} = \frac{5}{( 2 + i )}

x, 23 x + 29 y = 25

3 y \frac{1}{2} - y - 2 = 0

What is the answer to (x/((3+4i)))+(((2x+5i))/((1-2i)))=2+2i ?
The answer to (x/((3+4i)))+(((2x+5i))/((1-2i)))=2+2i is x=4-3i