What is sqrt(-1+\sqrt{-1)}^2 ?

The solution to sqrt(-1+\sqrt{-1)}^2 is -1+i

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simplify sqrt(-1+\sqrt{-1)}^2

simplify

- 1 + - 1^{2}

- 1 + i

Solution steps

(- 1 + - 1)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

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

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

\frac{1}{2} \cdot 2 = 1

= (- 1 + - 1)

Apply imaginary number rule:

- 1 = i

= - 1 + i

e^{- 368}

3^{2 m} \cdot 4^{2 m}

(7 + 3) (7 + 3)

3 s^{2} (3 s - 9 s^{2})^{2}