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Popular >

simplify (sqrt(-3))^4

Solution

simplify

(- 3)^{4}

Solution

9

Solution steps

(- 3)^{4}

- 3 = 3 i

= (3 i)^{4}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 i)^{4} = (3)^{4} i^{4}

= (3)^{4} i^{4}

(3)^{4} = 3^{2}

= 3^{2} i^{4}

3^{2} = 9

= 9 i^{4}

Apply exponent rule:

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

i^{4} = (i^{2})^{2}

= 9 (i^{2})^{2}

Apply imaginary number rule:

i^{2} = - 1

= 9 (- 1)^{2}

(- 1)^{2} = 1

= 9 \cdot 1

Multiply the numbers:

9 \cdot 1 = 9

= 9

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Frequently Asked Questions (FAQ)

What is (sqrt(-3))^4 ?
The solution to (sqrt(-3))^4 is 9