MAT334-2018F > Quiz-2

Q2 TUT 0201

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Victor Ivrii:
Find all points of continuity of the given function:
\begin{equation*}
f(z)=\left\{\begin{aligned}
&\frac{z^4-1}{z-i}, &&z\ne i\\
&4i, &&z=i.
\end{aligned}
\right.
\end{equation*}

Xier Li:
$(z^4-1)/(z-i) = z^3+iz^2-z-i$ when $z\ne i$.
When $z\to i$, $z^4-1)/(z-i) \to -4i$.
This contradicts the fact that $f(z)=4i$ when $z=i$.
Thus, the function is continuous everywhere except $z=i.$