What is (-2+4i)^{13} ?

The solution to (-2+4i)^{13} is 72409088+276905984i

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Popular Algebra >

simplify (-2+4i)^{13}

Solution

simplify

(- 2 + 4 i)^{13}

Solution

72409088 + 276905984 i

Solution steps

(- 2 + 4 i)^{13}

Apply binomial theorem:

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

a = - 2, b = 4 i

= i = 0 \sum 13 (i 13) (- 2)^{(13 - i)} (4 i)^{i}

Expand summation

= \frac{13 !}{0 ! ( 13 - 0 ) !} (- 2)^{13} (4 i)^{0} + \frac{13 !}{1 ! ( 13 - 1 ) !} (- 2)^{12} (4 i)^{1} + \frac{13 !}{2 ! ( 13 - 2 ) !} (- 2)^{11} (4 i)^{2} + \frac{13 !}{3 ! ( 13 - 3 ) !} (- 2)^{10} (4 i)^{3} + \frac{13 !}{4 ! ( 13 - 4 ) !} (- 2)^{9} (4 i)^{4} + \frac{13 !}{5 ! ( 13 - 5 ) !} (- 2)^{8} (4 i)^{5} + \frac{13 !}{6 ! ( 13 - 6 ) !} (- 2)^{7} (4 i)^{6} + \frac{13 !}{7 ! ( 13 - 7 ) !} (- 2)^{6} (4 i)^{7} + \frac{13 !}{8 ! ( 13 - 8 ) !} (- 2)^{5} (4 i)^{8} + \frac{13 !}{9 ! ( 13 - 9 ) !} (- 2)^{4} (4 i)^{9} + \frac{13 !}{10 ! ( 13 - 10 ) !} (- 2)^{3} (4 i)^{10} + \frac{13 !}{11 ! ( 13 - 11 ) !} (- 2)^{2} (4 i)^{11} + \frac{13 !}{12 ! ( 13 - 12 ) !} (- 2)^{1} (4 i)^{12} + \frac{13 !}{13 ! ( 13 - 13 ) !} (- 2)^{0} (4 i)^{13}

Simplify

\frac{13 !}{0 ! ( 13 - 0 ) !} (- 2)^{13} (4 i)^{0} : - 8192

Simplify

\frac{13 !}{1 ! ( 13 - 1 ) !} (- 2)^{12} (4 i)^{1} : 212992 i

Simplify

\frac{13 !}{2 ! ( 13 - 2 ) !} (- 2)^{11} (4 i)^{2} : - 2555904 i^{2}

Simplify

\frac{13 !}{3 ! ( 13 - 3 ) !} (- 2)^{10} (4 i)^{3} : 18743296 i^{3}

Simplify

\frac{13 !}{4 ! ( 13 - 4 ) !} (- 2)^{9} (4 i)^{4} : - 93716480 i^{4}

Simplify

\frac{13 !}{5 ! ( 13 - 5 ) !} (- 2)^{8} (4 i)^{5} : 337379328 i^{5}

Simplify

\frac{13 !}{6 ! ( 13 - 6 ) !} (- 2)^{7} (4 i)^{6} : - 899678208 i^{6}

Simplify

\frac{13 !}{7 ! ( 13 - 7 ) !} (- 2)^{6} (4 i)^{7} : 1799356416 i^{7}

Simplify

\frac{13 !}{8 ! ( 13 - 8 ) !} (- 2)^{5} (4 i)^{8} : - 2699034624 i^{8}

Simplify

\frac{13 !}{9 ! ( 13 - 9 ) !} (- 2)^{4} (4 i)^{9} : 2998927360 i^{9}

Simplify

\frac{13 !}{10 ! ( 13 - 10 ) !} (- 2)^{3} (4 i)^{10} : - 2399141888 i^{10}

Simplify

\frac{13 !}{11 ! ( 13 - 11 ) !} (- 2)^{2} (4 i)^{11} : 1308622848 i^{11}

Simplify

\frac{13 !}{12 ! ( 13 - 12 ) !} (- 2)^{1} (4 i)^{12} : - 436207616 i^{12}

Simplify

\frac{13 !}{13 ! ( 13 - 13 ) !} (- 2)^{0} (4 i)^{13} : 67108864 i^{13}

= - 8192 + 212992 i - 2555904 i^{2} + 18743296 i^{3} - 93716480 i^{4} + 337379328 i^{5} - 899678208 i^{6} + 1799356416 i^{7} - 2699034624 i^{8} + 2998927360 i^{9} - 2399141888 i^{10} + 1308622848 i^{11} - 436207616 i^{12} + 67108864 i^{13}

Simplify

- 8192 + 212992 i - 2555904 i^{2} + 18743296 i^{3} - 93716480 i^{4} + 337379328 i^{5} - 899678208 i^{6} + 1799356416 i^{7} - 2699034624 i^{8} + 2998927360 i^{9} - 2399141888 i^{10} + 1308622848 i^{11} - 436207616 i^{12} + 67108864 i^{13} : 276905984 i + 72409088

= 276905984 i + 72409088

Rewrite in standard complex form:

72409088 + 276905984 i

= 72409088 + 276905984 i

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Frequently Asked Questions (FAQ)

What is (-2+4i)^{13} ?
The solution to (-2+4i)^{13} is 72409088+276905984i

simplify (-2+4i)^{13}

Solution

Solution

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Frequently Asked Questions (FAQ)

What is (-2+4i)^{13} ?

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