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Math Help - complex number

  1. #1
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    complex number

    I have that f(z) = 1/(z+i) and I need to write f(z+i) as a(x,y) + i*b(x,y) where a and b are real functions.

    I see that f(z+i) = 1/(z+2i) and I multiplied by its conjugate z-2i, but since z is itself a complex number with x + iy, I don't see how I can separate f(z+i) into its real and complex part. Can someone help me here?

    Thanks in advance.
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    Hello,
    Quote Originally Posted by PvtBillPilgrim View Post
    I have that f(z) = 1/(z+i) and I need to write f(z+i) as a(x,y) + i*b(x,y) where a and b are real functions.

    I see that f(z+i) = 1/(z+2i) and I multiplied by its conjugate z-2i, but since z is itself a complex number with x + iy, I don't see how I can separate f(z+i) into its real and complex part. Can someone help me here?

    Thanks in advance.
    Write \frac{1}{z+2i}=\frac{1}{x+iy+2i}=\frac{1}{x+i(y+2)  }

    Here is your new complex number a+ib, where a=x and b=y+2.
    Multiply by the conjugate =)
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