Toronto Math Forum
MAT3342018F => MAT334Tests => Quiz2 => Topic started by: Victor Ivrii on October 05, 2018, 06:12:58 PM

Find all points of continuity of the given function:
\begin{equation*}
f(z)=\left\{\begin{aligned}
&\frac{z^41}{zi}, &&z\ne i\\
&4i, &&z=i.
\end{aligned}
\right.
\end{equation*}

$(z^41)/(zi) = z^3+iz^2zi$ when $z\ne i$.
When $z\to i$, $z^41)/(zi) \to 4i$.
This contradicts the fact that $f(z)=4i$ when $z=i$.
Thus, the function is continuous everywhere except $z=i.$