This is for a complex variable class and I have know idea how to sketch the doma

Question

This is for a complex variable class and I have know idea how to sketch the domain, please help!

Sketch the domain in the complex plane on which the function is defined.

2. f(z) = 2Log(z)

3. f(z) = z

Explanation / Answer

1. domain -> non zero denominator.. z^3 - 5iz^2+6z=0 => z(z^2 - 5iz +6)=0 z(z-(5i+1/2))(z-(5i-1)/2)=0 => domain is C-{0,5i+1/2, 5i-1/2} (C is the set of complex numbers) 2. f(z)= 2 log(z) z= r*e^(ix) f(z)= 2 log(r*e^(ix))= 2 log(r)+ 2ix so, the domain is C (C is the set of complex numbers) 3. f(z)= sqrt(r*e^(ix)) so, the domain is C (C is the set of complex numbers)

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