Does-the-function-f-z-3z-4-2z-3-8z-2-2z-5-z-i-continuous-at-z-i-

Question Number 128574 by mohammad17 last updated on 08/Jan/21

D o e s t h e f u n c t i o n f (z) = \frac{3 z^{4} - 2 z^{3} + 8 z^{2} - 2 z + 5}{z - i}

c o n t i n u o u s a t z = i ?

Answered by MJS_new last updated on 08/Jan/21

f (z) = \frac{(z^{2} + 1) (3 z^{2} - 2 z + 5)}{z - i} =

= \frac{(z - i) (z + i) (3 z^{2} - 2 z + 5)}{z - i} =

= (z + i) (3 z^{2} - 2 z + 5)

\Rightarrow f (z) is continuous at z = i

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