en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (4+3i)^6

Solution

simplify

(4 + 3 i)^{6}

Solution

- 11753 - 10296 i

Solution steps

(4 + 3 i)^{6}

Apply binomial theorem:

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

a = 4, b = 3 i

= i = 0 \sum 6 (i 6) \cdot 4^{(6 - i)} (3 i)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 4^{6} (3 i)^{0} : 4096

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 4^{5} (3 i)^{1} : 18432 i

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 4^{4} (3 i)^{2} : 34560 i^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 4^{3} (3 i)^{3} : 34560 i^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 4^{2} (3 i)^{4} : 19440 i^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 4^{1} (3 i)^{5} : 5832 i^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 4^{0} (3 i)^{6} : 729 i^{6}

= 4096 + 18432 i + 34560 i^{2} + 34560 i^{3} + 19440 i^{4} + 5832 i^{5} + 729 i^{6}

Simplify

4096 + 18432 i + 34560 i^{2} + 34560 i^{3} + 19440 i^{4} + 5832 i^{5} + 729 i^{6} : - 10296 i - 11753

= - 10296 i - 11753

Rewrite in standard complex form:

- 11753 - 10296 i

= - 11753 - 10296 i

Popular Examples

expand (28500+1000ln(33/14))(1/57)expand

(28500 + 1000 ln (\frac{33}{14})) (\frac{1}{57})

(d^2)/(dx^2)((y)(x^2-1)^3)

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

expand (e^{2x})(x/4+A)+(e^{-2x})(1/16 e^{4x}+B)expand

(e^{2 x}) (\frac{x}{4} + A) + (e^{- 2 x}) (\frac{1}{16} e^{4 x} + B)

(d^2)/(dx^2)((y)((a*x)+((1-a)*x^2)))

\frac{d ^{2}}{d x ^{2}} ((y) ((a \cdot x) + ((1 - a) \cdot x^{2})))

(\partial)/(\partial v)((x)(9u+2v))

\frac{\partial}{\partial v} ((x) (9 u + 2 v))

Frequently Asked Questions (FAQ)

What is (4+3i)^6 ?
The solution to (4+3i)^6 is -11753-10296i