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Popular >

simplify (-5-6i)^4

Solution

simplify

(- 5 - 6 i)^{4}

Solution

- 3479 - 1320 i

Solution steps

(- 5 - 6 i)^{4}

Apply binomial theorem:

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

a = - 5, b = - 6 i

= i = 0 \sum 4 (i 4) (- 5)^{(4 - i)} (- 6 i)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 5)^{4} (- 6 i)^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (- 5)^{3} (- 6 i)^{1} : 3000 i

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 5)^{2} (- 6 i)^{2} : 5400 i^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (- 5)^{1} (- 6 i)^{3} : 4320 i^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 5)^{0} (- 6 i)^{4} : 1296 i^{4}

= 625 + 3000 i + 5400 i^{2} + 4320 i^{3} + 1296 i^{4}

Simplify

625 + 3000 i + 5400 i^{2} + 4320 i^{3} + 1296 i^{4} : - 1320 i - 3479

= - 1320 i - 3479

Rewrite in standard complex form:

- 3479 - 1320 i

= - 3479 - 1320 i

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Frequently Asked Questions (FAQ)

What is (-5-6i)^4 ?
The solution to (-5-6i)^4 is -3479-1320i