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

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

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

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

- 4 i

Solution steps

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

Rationalize denominator

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

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

Plug in the value

z = i

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

Simplify

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

= - 4 i

x \to - \infty lim (\frac{x}{1})

x \to 0 lim (\frac{1}{x sin ( x )})

x \to 0 + lim (\frac{1}{1 + 3 ^{\frac{1}{x}}})

x \to 0 lim (\frac{e ^{x - 1}}{x})

x \to - 2 + lim (\frac{1}{4 - x ^{2}})

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