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Math Help - Complex Differentiation Properties

  1. #1
    Senior Member bugatti79's Avatar
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    Complex Differentiation Properties

    Hi Folks,

    Use the properties of complex differentiation to calculate f'(z) for the following

    a) (3-2i)z+4i, b) z^3-(2+i)z^2+(1+3i)z-1

    Not sure how to tackle these. My attempt -

    Using the property similar to real values differentiable functions \frac{d f(Az)}{dz} where A is a constant we have for

    a) (3-2i)

    b) 3z^2 -2z(2+i)+(1+3i)...?

    Thanks
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  2. #2
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    Re: Complex Differentiation Properties

    That looks good to me?
    For a, we assume everything but z is constant, thus 4i goes to zero and (3-2i)z differentiates to (3-2i)
    differentiate (3-2i)z+4i - Wolfram|Alpha

    For b, it should be:
    3z^2 -2(2+i)z + (1+3i), which is what you have. Yep all looks good to me?
    differentiate z^3-(2+i)z^2+(1+3i)z-1 - Wolfram|Alpha
    Thanks from bugatti79
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