en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2-i)^7

Solution

simplify

(2 - i)^{7}

Solution

- 278 + 29 i

Solution steps

(2 - i)^{7}

Apply binomial theorem:

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

a = 2, b = - i

= i = 0 \sum 7 (i 7) \cdot 2^{(7 - i)} (- i)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (- i)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (- i)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (- i)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (- i)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (- i)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (- i)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (- i)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (- i)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (- i)^{0} : 128

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (- i)^{1} : - 448 i

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (- i)^{2} : 672 i^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (- i)^{3} : - 560 i^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (- i)^{4} : 280 i^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (- i)^{5} : - 84 i^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (- i)^{6} : 14 i^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (- i)^{7} : - i^{7}

= 128 - 448 i + 672 i^{2} - 560 i^{3} + 280 i^{4} - 84 i^{5} + 14 i^{6} - i^{7}

Simplify

128 - 448 i + 672 i^{2} - 560 i^{3} + 280 i^{4} - 84 i^{5} + 14 i^{6} - i^{7} : 29 i - 278

= 29 i - 278

Rewrite in standard complex form:

- 278 + 29 i

= - 278 + 29 i

Popular Examples

expand (xy^2-y^2+x-1)dx+(x^2y-2xy+x^2+2y-2x+2)dy expand

(x y^{2} - y^{2} + x - 1) d x + (x^{2} y - 2 x y + x^{2} + 2 y - 2 x + 2) d y

simplify (-1+2i)^{15}simplify

(- 1 + 2 i)^{15}

expand 12(1-e^{-t/τ})expand

12 (1 - e^{- \frac{t}{τ}})

simplify 3(3-sqrt(3))simplify

3 (3 - 3)

simplify (cos(x)+cos(y))^2+(sin(x)+sin(y))^2 simplify

(cos (x) + cos (y))^{2} + (sin (x) + sin (y))^{2}

Frequently Asked Questions (FAQ)

What is (2-i)^7 ?
The solution to (2-i)^7 is -278+29i