What is sqrt(-1)sqrt(-1)sqrt(-1) ?

The solution to sqrt(-1)sqrt(-1)sqrt(-1) is -i

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simplify sqrt(-1)sqrt(-1)sqrt(-1)

simplify

- 1 - 1 - 1

- i

Solution steps

- 1 - 1 - 1

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

- 1 - 1 - 1 = (- 1)^{\frac{1}{2}} (- 1)^{\frac{1}{2}} (- 1)^{\frac{1}{2}} = (- 1)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

= (- 1)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Combine the fractions

\frac{1}{2} + \frac{1}{2} + \frac{1}{2} : \frac{3}{2}

= (- 1)^{\frac{3}{2}}

Apply exponent rule:

a^{\frac{m}{n}} = (a^{\frac{1}{n}})^{m}

(- 1)^{\frac{3}{2}} = (- 1)^{3}

= (- 1)^{3}

Apply imaginary number rule:

- 1 = i

= i^{3}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

i^{3} = i^{2} i

= i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= - 1 i

Multiply:

1 i = i

= - i

e^{- 3 l n (2)}

0.9 \cdot 1 0^{- 2}

81

What is sqrt(-1)sqrt(-1)sqrt(-1) ?
The solution to sqrt(-1)sqrt(-1)sqrt(-1) is -i