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Popular >

simplify (-8-9i)^6

Solution

simplify

(- 8 - 9 i)^{6}

Solution

1052623 - 2861136 i

Solution steps

(- 8 - 9 i)^{6}

Apply binomial theorem:

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

a = - 8, b = - 9 i

= i = 0 \sum 6 (i 6) (- 8)^{(6 - i)} (- 9 i)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (- 8)^{6} (- 9 i)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (- 8)^{5} (- 9 i)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (- 8)^{4} (- 9 i)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (- 8)^{3} (- 9 i)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (- 8)^{2} (- 9 i)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (- 8)^{1} (- 9 i)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (- 8)^{0} (- 9 i)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (- 8)^{6} (- 9 i)^{0} : 262144

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (- 8)^{5} (- 9 i)^{1} : 1769472 i

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (- 8)^{4} (- 9 i)^{2} : 4976640 i^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (- 8)^{3} (- 9 i)^{3} : 7464960 i^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (- 8)^{2} (- 9 i)^{4} : 6298560 i^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (- 8)^{1} (- 9 i)^{5} : 2834352 i^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (- 8)^{0} (- 9 i)^{6} : 531441 i^{6}

= 262144 + 1769472 i + 4976640 i^{2} + 7464960 i^{3} + 6298560 i^{4} + 2834352 i^{5} + 531441 i^{6}

Simplify

262144 + 1769472 i + 4976640 i^{2} + 7464960 i^{3} + 6298560 i^{4} + 2834352 i^{5} + 531441 i^{6} : - 2861136 i + 1052623

= - 2861136 i + 1052623

Rewrite in standard complex form:

1052623 - 2861136 i

= 1052623 - 2861136 i

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Frequently Asked Questions (FAQ)

What is (-8-9i)^6 ?
The solution to (-8-9i)^6 is 1052623-2861136i