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Popular >

simplify (-3-2i)^8

Solution

simplify

(- 3 - 2 i)^{8}

Solution

- 239 - 28560 i

Solution steps

(- 3 - 2 i)^{8}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = - 3, b = - 2 i

= i = 0 \sum 8 (i 8) (- 3)^{(8 - i)} (- 2 i)^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} (- 3)^{8} (- 2 i)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} (- 3)^{7} (- 2 i)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} (- 3)^{6} (- 2 i)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} (- 3)^{5} (- 2 i)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} (- 3)^{4} (- 2 i)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} (- 3)^{3} (- 2 i)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} (- 3)^{2} (- 2 i)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} (- 3)^{1} (- 2 i)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} (- 3)^{0} (- 2 i)^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (- 3)^{8} (- 2 i)^{0} : 6561

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (- 3)^{7} (- 2 i)^{1} : 34992 i

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (- 3)^{6} (- 2 i)^{2} : 81648 i^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (- 3)^{5} (- 2 i)^{3} : 108864 i^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (- 3)^{4} (- 2 i)^{4} : 90720 i^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (- 3)^{3} (- 2 i)^{5} : 48384 i^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (- 3)^{2} (- 2 i)^{6} : 16128 i^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (- 3)^{1} (- 2 i)^{7} : 3072 i^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (- 3)^{0} (- 2 i)^{8} : 256 i^{8}

= 6561 + 34992 i + 81648 i^{2} + 108864 i^{3} + 90720 i^{4} + 48384 i^{5} + 16128 i^{6} + 3072 i^{7} + 256 i^{8}

Simplify

6561 + 34992 i + 81648 i^{2} + 108864 i^{3} + 90720 i^{4} + 48384 i^{5} + 16128 i^{6} + 3072 i^{7} + 256 i^{8} : - 28560 i - 239

= - 28560 i - 239

Rewrite in standard complex form:

- 239 - 28560 i

= - 239 - 28560 i

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Frequently Asked Questions (FAQ)

What is (-3-2i)^8 ?
The solution to (-3-2i)^8 is -239-28560i