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

$$Doesthefunctionf\left(z\right)=\frac{3z^4-2z^3+8z^2-2z+5}{z-i}$$$$$$$$continuousatz=i?$$

Answered by MJS_new last updated on 08/Jan/21

$$f\left(z\right)=\frac{(z^2+1)(3z^2-2z+5)}{z-\mathrm{i}}=$$$$=\frac{(z-\mathrm{i})(z+\mathrm{i})(3z^2-2z+5)}{z-\mathrm{i}}=$$$$=(z+\mathrm{i})(3z^2-2z+5)$$$$\Rightarrow f\left(z\right)\mathrm{is}\mathrm{continuous}\mathrm{at}z=\mathrm{i}$$

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