when $\displaystyle r\to 0~?$, $\displaystyle z=re^{\mathif{i}\theta}$ then $\displaystyle \frac{z\cdot\text{Re}(z)}{|z|}=\frac{(re^{\mathif{ i}\theta})(r\cos(\theta)}{r}$=infinity???I think so.
Oh my no.
Is this true: $\displaystyle r\not= 0$ so $\displaystyle \frac{(re^{\mathif{i}\theta})(r\cos(\theta)}{r}=(r e^{\mathif{i}\theta})(\cos(\theta))~?$
Oh my no.
Is this true: $\displaystyle r\not= 0$ so $\displaystyle \frac{(re^{\mathif{i}\theta})(r\cos(\theta)}{r}=(r e^{\mathif{i}\theta})(\cos(\theta))~?$
What is there to prove.
As $\displaystyle r\to 0$ the other factors are bounded, so what is the limit?
Sorry sir,i dont know.i am not dat good in maths.please help me.
Edit : As $\displaystyle r\to 0$ the other factors are bounded,means a finite limit.Is it so?
Limit is 0 and hence the function is continuous in the entire complex plane.Am i right?
Last edited by deepakpc007; Apr 29th 2011 at 05:53 AM.