What is the limit as x approaches-i of (x^4-1)/(x+i) ?

The limit as x approaches-i of (x^4-1)/(x+i) is 4i

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limit as x approaches-i of (x^4-1)/(x+i)

x \to - i lim (\frac{x ^{4} - 1}{x + i})

4 i

Solution steps

x \to - i lim (\frac{x ^{4} - 1}{x + i})

Rationalize denominator

\frac{x ^{4} - 1}{x + i} : (x^{3} - x) + i (1 - x^{2})

= x \to - i lim (x^{3} - x + i (1 - x^{2}))

Plug in the value

x = - i

= (- i)^{3} - (- i) + i (1 - (- i)^{2})

Simplify

(- i)^{3} - (- i) + i (1 - (- i)^{2}) : 4 i

= 4 i

What is the limit as x approaches-i of (x^4-1)/(x+i) ?
The limit as x approaches-i of (x^4-1)/(x+i) is 4i