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Popular >

simplify (-2i)^3

Solution

simplify

(- 2 i)^{3}

Solution

8 i

Solution steps

(- 2 i)^{3}

Apply exponent rule:

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

if

n

is odd

(- 2 i)^{3} = - (2 i)^{3}

= - (2 i)^{3}

Apply exponent rule:

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

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

= - 2^{3} i^{3}

2^{3} = 8

= - 8 i^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

i^{3} = i^{2} i

= - 8 i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= - 8 (- 1 i)

Apply rule:

1 \cdot a = a

- 1 i = - i

= - 8 (- i)

Apply rule:

- a (- b) = ab

- 8 (- i) = 8 i

= 8 i

Popular Examples

2 7^{2} + x^{2} = 4 5^{2}

simplify (x^{2/3})^{1/2}simplify

(x^{\frac{2}{3}})^{\frac{1}{2}}

x^2-5/2 x-11/16 =0

x^{2} - \frac{5}{2} x - \frac{11}{16} = 0

- 8 t > 5

11 x^{2} - 11 x + 8 = 4

Frequently Asked Questions (FAQ)

What is (-2i)^3 ?
The solution to (-2i)^3 is 8i