What is expand (-2.5099+6.2121i)^5 ?

The solution to expand (-2.5099+6.2121i)^5 is -12686.71812…-4618.07173…i

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expand (-2.5099+6.2121i)^5

expand

(- 2.5099 + 6.2121 i)^{5}

- 12686.71812 \dots - 4618.07173 \dots i

Solution steps

(- 2.5099 + 6.2121 i)^{5}

Apply binomial theorem:

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

a = - 2.5099, b = 6.2121 i

= i = 0 \sum 5 (i 5) (- 2.5099)^{(5 - i)} (6.2121 i)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (- 2.5099)^{5} (6.2121 i)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (- 2.5099)^{4} (6.2121 i)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (- 2.5099)^{3} (6.2121 i)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (- 2.5099)^{2} (6.2121 i)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (- 2.5099)^{1} (6.2121 i)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (- 2.5099)^{0} (6.2121 i)^{5}

\frac{5 !}{0 ! ( 5 - 0 ) !} (- 2.5099)^{5} (6.2121 i)^{0} = - 99.60521 \dots

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (- 2.5099)^{4} (6.2121 i)^{1} : 1232.63392 \dots i

\frac{5 !}{2 ! ( 5 - 2 ) !} (- 2.5099)^{3} (6.2121 i)^{2} = 6101.63370 \dots

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (- 2.5099)^{2} (6.2121 i)^{3} : - 15101.78043 \dots i

\frac{5 !}{4 ! ( 5 - 4 ) !} (- 2.5099)^{1} (6.2121 i)^{4} = - 18688.74661 \dots

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (- 2.5099)^{0} (6.2121 i)^{5} : 9251.07477 \dots i

= - 99.60521 \dots + 1232.63392 \dots i + 6101.63370 \dots - 15101.78043 \dots i - 18688.74661 \dots + 9251.07477 \dots i

Simplify

- 99.60521 \dots + 1232.63392 \dots i + 6101.63370 \dots - 15101.78043 \dots i - 18688.74661 \dots + 9251.07477 \dots i : - 12686.71812 \dots - 4618.07173 \dots i

= - 12686.71812 \dots - 4618.07173 \dots i

(5 p + q) (5 p - q)

U (1, 2) V (- 3, 4) W (- 1, - 2) U + V + W

\frac{x + h ( x ) + 1 - ( x + 1 )}{h ( x )}

(u + v + w) (\frac{v + u + 1}{( u + v ) ^{2}})

f (x) = d x (5 x^{2} + 2 x + 1)^{3} + ln (x + 1)

What is expand (-2.5099+6.2121i)^5 ?
The solution to expand (-2.5099+6.2121i)^5 is -12686.71812…-4618.07173…i