What is sqrt(-1)^{164} ?

The solution to sqrt(-1)^{164} is 1

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simplify sqrt(-1)^{164}

simplify

- 1^{164}

1

Solution steps

(- 1)^{164}

Apply imaginary number rule:

- 1 = i

= i^{164}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

i^{164} = (i^{2})^{82}

= (i^{2})^{82}

Apply imaginary number rule:

i^{2} = - 1

= (- 1)^{82}

(- 1)^{82} = 1

= 1

x + 1 \cdot 1 + \frac{1}{4 x + 4}

90.89 \cdot 1 0^{- 4} \frac{1}{0.833 \cdot 1.6 \cdot 1 0 ^{- 12}} \cdot \frac{1}{8 \cdot 1 0 ^{6}}

3 (7.2 \times 1 0^{- 6})

e^{- z^{2}}