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Popular >

simplify (-3i)^4

Solution

simplify

(- 3 i)^{4}

Solution

81

Solution steps

(- 3 i)^{4}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

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

= (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} = 81

= 81 i^{4}

Apply exponent rule:

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

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

= 81 (i^{2})^{2}

Apply imaginary number rule:

i^{2} = - 1

= 81 (- 1)^{2}

(- 1)^{2} = 1

= 81 \cdot 1

Multiply the numbers:

81 \cdot 1 = 81

= 81

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Frequently Asked Questions (FAQ)

What is (-3i)^4 ?
The solution to (-3i)^4 is 81