What is (1-3i)^{15} ?

The solution to (1-3i)^{15} is 31417984+3593088i

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Popular Algebra >

simplify (1-3i)^{15}

Solution

simplify

(1 - 3 i)^{15}

Solution

31417984 + 3593088 i

Solution steps

(1 - 3 i)^{15}

Apply binomial theorem:

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

a = 1, b = - 3 i

= i = 0 \sum 15 (i 15) \cdot 1^{(15 - i)} (- 3 i)^{i}

Expand summation

= \frac{15 !}{0 ! ( 15 - 0 ) !} \cdot 1^{15} (- 3 i)^{0} + \frac{15 !}{1 ! ( 15 - 1 ) !} \cdot 1^{14} (- 3 i)^{1} + \frac{15 !}{2 ! ( 15 - 2 ) !} \cdot 1^{13} (- 3 i)^{2} + \frac{15 !}{3 ! ( 15 - 3 ) !} \cdot 1^{12} (- 3 i)^{3} + \frac{15 !}{4 ! ( 15 - 4 ) !} \cdot 1^{11} (- 3 i)^{4} + \frac{15 !}{5 ! ( 15 - 5 ) !} \cdot 1^{10} (- 3 i)^{5} + \frac{15 !}{6 ! ( 15 - 6 ) !} \cdot 1^{9} (- 3 i)^{6} + \frac{15 !}{7 ! ( 15 - 7 ) !} \cdot 1^{8} (- 3 i)^{7} + \frac{15 !}{8 ! ( 15 - 8 ) !} \cdot 1^{7} (- 3 i)^{8} + \frac{15 !}{9 ! ( 15 - 9 ) !} \cdot 1^{6} (- 3 i)^{9} + \frac{15 !}{10 ! ( 15 - 10 ) !} \cdot 1^{5} (- 3 i)^{10} + \frac{15 !}{11 ! ( 15 - 11 ) !} \cdot 1^{4} (- 3 i)^{11} + \frac{15 !}{12 ! ( 15 - 12 ) !} \cdot 1^{3} (- 3 i)^{12} + \frac{15 !}{13 ! ( 15 - 13 ) !} \cdot 1^{2} (- 3 i)^{13} + \frac{15 !}{14 ! ( 15 - 14 ) !} \cdot 1^{1} (- 3 i)^{14} + \frac{15 !}{15 ! ( 15 - 15 ) !} \cdot 1^{0} (- 3 i)^{15}

Simplify

\frac{15 !}{0 ! ( 15 - 0 ) !} \cdot 1^{15} (- 3 i)^{0} : 1

Simplify

\frac{15 !}{1 ! ( 15 - 1 ) !} \cdot 1^{14} (- 3 i)^{1} : - 45 i

Simplify

\frac{15 !}{2 ! ( 15 - 2 ) !} \cdot 1^{13} (- 3 i)^{2} : 945 i^{2}

Simplify

\frac{15 !}{3 ! ( 15 - 3 ) !} \cdot 1^{12} (- 3 i)^{3} : - 12285 i^{3}

Simplify

\frac{15 !}{4 ! ( 15 - 4 ) !} \cdot 1^{11} (- 3 i)^{4} : 110565 i^{4}

Simplify

\frac{15 !}{5 ! ( 15 - 5 ) !} \cdot 1^{10} (- 3 i)^{5} : - 729729 i^{5}

Simplify

\frac{15 !}{6 ! ( 15 - 6 ) !} \cdot 1^{9} (- 3 i)^{6} : 3648645 i^{6}

Simplify

\frac{15 !}{7 ! ( 15 - 7 ) !} \cdot 1^{8} (- 3 i)^{7} : - 14073345 i^{7}

Simplify

\frac{15 !}{8 ! ( 15 - 8 ) !} \cdot 1^{7} (- 3 i)^{8} : 42220035 i^{8}

Simplify

\frac{15 !}{9 ! ( 15 - 9 ) !} \cdot 1^{6} (- 3 i)^{9} : - 98513415 i^{9}

Simplify

\frac{15 !}{10 ! ( 15 - 10 ) !} \cdot 1^{5} (- 3 i)^{10} : 177324147 i^{10}

Simplify

\frac{15 !}{11 ! ( 15 - 11 ) !} \cdot 1^{4} (- 3 i)^{11} : - 241805655 i^{11}

Simplify

\frac{15 !}{12 ! ( 15 - 12 ) !} \cdot 1^{3} (- 3 i)^{12} : 241805655 i^{12}

Simplify

\frac{15 !}{13 ! ( 15 - 13 ) !} \cdot 1^{2} (- 3 i)^{13} : - 167403915 i^{13}

Simplify

\frac{15 !}{14 ! ( 15 - 14 ) !} \cdot 1^{1} (- 3 i)^{14} : 71744535 i^{14}

Simplify

\frac{15 !}{15 ! ( 15 - 15 ) !} \cdot 1^{0} (- 3 i)^{15} : - 14348907 i^{15}

= 1 - 45 i + 945 i^{2} - 12285 i^{3} + 110565 i^{4} - 729729 i^{5} + 3648645 i^{6} - 14073345 i^{7} + 42220035 i^{8} - 98513415 i^{9} + 177324147 i^{10} - 241805655 i^{11} + 241805655 i^{12} - 167403915 i^{13} + 71744535 i^{14} - 14348907 i^{15}

Simplify

1 - 45 i + 945 i^{2} - 12285 i^{3} + 110565 i^{4} - 729729 i^{5} + 3648645 i^{6} - 14073345 i^{7} + 42220035 i^{8} - 98513415 i^{9} + 177324147 i^{10} - 241805655 i^{11} + 241805655 i^{12} - 167403915 i^{13} + 71744535 i^{14} - 14348907 i^{15} : 3593088 i + 31417984

= 3593088 i + 31417984

Rewrite in standard complex form:

31417984 + 3593088 i

= 31417984 + 3593088 i

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Frequently Asked Questions (FAQ)

What is (1-3i)^{15} ?
The solution to (1-3i)^{15} is 31417984+3593088i

simplify (1-3i)^{15}

Solution

Solution

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Frequently Asked Questions (FAQ)

What is (1-3i)^{15} ?

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