# Thread: Complex Differentiation Properties

1. ## 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

2. ## 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