Complex functions & Limits: (2) Let $a,b$ be complex constants. Show that $$\lim_{z\rightarrow z_0} (az+b)=az_0+b$$ (7) Use the definition of limit to prove that if $\displaystyle \lim_{z\rightarrow z_0} f(z)=w_0$ then $$\displaystyle \lim_{z\rightarrow z_0} \left|f(z)\right|=\left|w_0\right|$$

QUESTIONS:

(2)  Let $a,b$ be complex constants. Show that $$\lim_{z\rightarrow z_0} (az+b)=az_0+b$$

(7) Use the definition of limit to prove that if $\displaystyle \lim_{z\rightarrow z_0} f(z)=w_0$ then 

$$\displaystyle \lim_{z\rightarrow z_0} \left|f(z)\right|=\left|w_0\right|$$

APPENDIX  ==============================