MAT334--2020S > Quiz 2

TUT5101 QUIZ2

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**Yiheng Bian**:

Question:

$$

h(z)=\frac{Log(z)}{z}

$$

We know when

$$

z \rightarrow \infty

$$

$$

Log(z) \rightarrow \infty

$$

So we can use L'Hopital rules and get

$$

\frac{1}{z}

$$

So

$$

\text{limit is zero}

$$

**Victor Ivrii**:

Wrong reasoning

**Yiheng Bian**:

Sorry sir, , could you point it out?

**Victor Ivrii**:

You cannot use LH out of the box for complex variables. You need to consider $z=re^{i\theta}$ and consider $\bigl|\dfrac{\operatorname{Log}(z)}{z}\bigr|$ ...

**Yiheng Bian**:

Ok, I got it. Thank you sir

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