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Popular >

simplify (sqrt(1+\sqrt{-3)})^2

Solution

simplify

(1 + - 3)^{2}

Solution

1 + 3 i

Solution steps

(1 + - 3)^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

= 1 + - 3

- 3 = 3 i

= 1 + 3 i

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Frequently Asked Questions (FAQ)

What is (sqrt(1+\sqrt{-3)})^2 ?
The solution to (sqrt(1+\sqrt{-3)})^2 is 1+sqrt(3)i