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Popular >

simplify (sqrt(2))^i

Solution

simplify

(2)^{i}

Solution

2^{\frac{i}{2}}

Solution steps

(2)^{i}

Apply radical rule:

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

= (2^{\frac{1}{2}})^{i}

Apply exponent rule:

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

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

Simplify

\frac{1}{2} i : \frac{i}{2}

= 2^{\frac{i}{2}}

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Frequently Asked Questions (FAQ)

What is (sqrt(2))^i ?
The solution to (sqrt(2))^i is 2^{i/2}