Complex Ratio

Algebra Level 2

Simplify $\large \frac{x^2 + 1}{x - i} .$

Notation: $i=\sqrt{-1}$ denotes the imaginary unit .

x - i

x + i

x + \frac{i + 1}{\sqrt{2}}

x - \frac{i + 1}{\sqrt{2}}

1 solution

Chew-Seong Cheong
Jan 16, 2017

$\begin{aligned} \frac {x^2+1}{x-i} & = \frac {(x-i)(x+i)}{x-i} & \small \color{#3D99F6} \text{For }x \ne i \\ & = \frac {(\cancel{x-i})(x+i)}{\cancel{x-i}} \\ & = \boxed{x+i} \end{aligned}$

I suppose to be precise it should be stated that this is only the case for $x \ne i$ , as there would be a point of discontinuity at this value.

Brian Charlesworth - 4 years, 4 months ago

Thanks. I have added a comment in the solution.

Chew-Seong Cheong - 4 years, 4 months ago

Complex Ratio

1 solution

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