Solve the equation (y - i)/(x - 3i) = 2+i

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation `(y - i)/(x - 3i) = 2+i` has to be solved.

`(y - i)/(x - 3i) = 2 + i`

=> `y - i = (2 + i)(x - 3i)`

=> `y - i = 2x - 6i + x*i - 3i^2`

=> `y - i = 2x - 6i + x*i + 3`

Equate the real and complex coefficients, this gives:

y = 2x + 3 and -1 = x - 6

x = 6 - 1 = 5

y = 2*5 + 3 = 13

The solution of the equation `(y - i)/(x - 3i) = 2 + i` is x = 5 and y = 13

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oldnick | (Level 1) Valedictorian

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`(y-i)/(x-3i)=2+i`

`(y-i)/(2+i)=x-3i`

`((y-i)(2-i))/(4-i^2)=x-3i`

`(2y-iy-2i+i^2)/5=x-3i`

`2y-iy-2i-1=5(x-3i)`

`2y-1-i(2+y)=5x-15i`

`5x-2y+1+i(y-13)=0`

this gives an system in two unknowns values:

`y-13=0`                     `=> y=13`

`5x-2y+1=0`             `=>5x-26+1=0` `=> x=5` 

So the solution is : 

`x=5; y=13`

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