SOLUTION: im really confused when it comes to complex numbers this is one of the questions (3-2i)x+3=(4+3i)x-4i so my teacher showed us to distribute then to get the x's on one side and t

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: im really confused when it comes to complex numbers this is one of the questions (3-2i)x+3=(4+3i)x-4i so my teacher showed us to distribute then to get the x's on one side and t      Log On


   

Question 386387: im really confused when it comes to complex numbers
this is one of the questions
(3-2i)x+3=(4+3i)x-4i
so my teacher showed us to distribute then to get the x's on one side and the non x's so i've got
-1x-ix=-4i-3
i would then multiply by a zero to get
x+ix=4i-3
after that im completly lost
Found 3 solutions by solver91311, scott8148, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Remember being told to be careful with signs when working with equations, especially when adding to both sides of an equation? Well, that goes double for working with complex coefficients.

Let's start again and take it one step at a time.



Distribute:



x terms on the left, constants on the right:



Collect likes:



Factor out the :



Divide by the coefficient on :



Not done yet. You need to rationalize the denominator. The trick here is to multiply your fraction by 1, but in the form of the conjugate of the denominator. The reason we use the conjugate is because the product of two conjugates is the difference of two squares and that gets rid of the imaginary term. Use FOIL to multiply a pair of complex numbers. Remember





John

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Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
distributing ___ 3x - 2xi + 3 = 4x + 3xi - 4i ___ 4i + 3 = x + 5xi

factoring ___ 4i + 3 = x(1 + 5i)

dividing by (1 + 5i) ___ (4i + 3) / (1 + 5i) = x

multiplying right side by (1 - 5i) / (1 - 5i) ___ (23 - 11i) / 26 = x

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!





(3 - 2i)x + 3 = (4 + 3i)x - 4i

 3x - 2ix + 3 = 4x + 3ix - 4i



3x - 2ix - 4x - 3ix = -3 - 4i



          -x - 5ix = -3 - 4i



        x(-1 - 5i) = -3 - 4i



                  x = %28-3-4i%29%2F%28-1-5i%29



Multiply by the conjugate of the denominator over itself:



                  x = %28-3-4i%29%2F%28-1-5i%29%28-1%2B5i%29%2F%28-1%2B5i%29



                  x = %283-15i%2B4i-20i%5E2%29%2F%281-5i%2B5i-25i%5E2%29



                  x = %283-11i-20i%5E2%29%2F%281-25i%5E2%29



Replace iČ by -1



                  x = %283-11i-20%28-1%29%29%2F%281-25%28-1%29%29



                  x = 3-11i%2B20%29%2F%281%2B25%29



                  x = 23-11i%29%2F26



                  x = 23%2F26-expr%2811%2F26%29i 

                  

Checking:



%283+-+2i%29x+%2B+3+=+%284+%2B+3i%29x+-+4i











Change iČ to -1







47%2F26-expr%2879%2F26%29i+%2B+3=125%2F26%2Bexpr%2825%2F26%29i-4i



Write 3 as 78%2F26 and -4i as -expr%28104%2F26%29i



47%2F26-expr%2879%2F26%29i+%2B+78%2F26=125%2F26%2Bexpr%2825%2F26%29i-expr%28104%2F26%29i



125%2F26-expr%2879%2F26%29i+=+125%2F26-expr%2879%2F26%29i