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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    To every complex number , z different from -i . assign
    f(z) = \frac{iz}{z+i}
    Denote by M the point of the plane with affix z .
    A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.
    Work !

    Affix of B is z0 = xB + iyB
    f(z0) = yB = 1 + 2i ..
    From the question : Solution : means that if I replace the values I will get zero
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  2. #2
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    Quote Originally Posted by Aladdin View Post
    To every complex number , z different from -i . assign
    f(z) = \frac{iz}{z+i}
    Denote by M the point of the plane with affix z .
    A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.
    Work !

    Affix of B is z0 = xB + iyB
    f(z0) = yB = 1 + 2i ..
    From the question : Solution : means that if I replace the values I will get zero
    So you are asked to solve the equation \frac{iz}{z+ i}= 1+ 2i.

    Basically, you solve this like you would any equation. Multiply on both sides by z+ i: iz= (1+2i)(z+ i)= (1+2i)z+ i- 2. Subtract (1+ 2i)z from both sides: iz- (1+2i)z= (-1- i)z= -2+ i. Divide both sides by -1-i: z= \frac{-2+ i}{-1-i}. You can "rationalize" the denominator of that fraction by multiplying both numerator and denominator by the conjugate of -1- i.
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  3. #3
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    Thank You -- We solved it in class and You're correct
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