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rmtzlr
rmtzlr asked in Science & MathematicsMathematics · 1 decade ago

Help me with complex equations:?

This one should be fun:

(x + iy + 2 + 3i)

---------------------- = i + 2

(2x + 2iy - 3)

Solve for x and y.

I know that this is a might be a lot of tedious algebra, but if you are willing to write it out and explain the approach you took, I will gladly give you 10 points. Thanks

1 Answer

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  • gp4rts
    Lv 7
    1 decade ago
    Favorite Answer

    First multiply both sides by the denominator 2x + 2iy - 3 to get

    x +iy +2 + 3i = (2x + 2iy - 3)*(i + 2)

    x +iy +2 + 3i = 2xi - 2y - 3i + 4x + 4iy - 6

    Collect terms:

    -3x -3iy - 2ix + 8 +6i = 0

    Separate into real and imaginary parts:

    (-3x + 8) + (-3y -2x + 6)i = 0

    Set the real and imaginary parts each to zero. The real part gives us the value of x

    x = 8/3

    Put this into the imaginary part

    -3y - 16/3 + 6 = 0

    -9y - 16 + 18 = 0

    -9y = -2

    y = 2/9

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