What is expand (9.3+2.1i)^4 ?

The solution to expand (9.3+2.1i)^4 is 5211.4428+6412.0896i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (9.3+2.1i)^4

expand

(9.3 + 2.1 i)^{4}

5211.4428 + 6412.0896 i

Solution steps

(9.3 + 2.1 i)^{4}

Apply binomial theorem:

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

a = 9.3, b = 2.1 i

= i = 0 \sum 4 (i 4) \cdot 9. 3^{(4 - i)} (2.1 i)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 9. 3^{4} (2.1 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 9. 3^{3} (2.1 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 9. 3^{2} (2.1 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 9. 3^{1} (2.1 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 9. 3^{0} (2.1 i)^{4}

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 9. 3^{4} (2.1 i)^{0} = 7480.5201

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 9. 3^{3} (2.1 i)^{1} : 6756.5988 i

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 9. 3^{2} (2.1 i)^{2} = - 2288.5254

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 9. 3^{1} (2.1 i)^{3} : - 344.5092 i

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 9. 3^{0} (2.1 i)^{4} = 19.4481

= 7480.5201 + 6756.5988 i - 2288.5254 - 344.5092 i + 19.4481

Simplify

7480.5201 + 6756.5988 i - 2288.5254 - 344.5092 i + 19.4481 : 5211.4428 + 6412.0896 i

= 5211.4428 + 6412.0896 i

(2 x^{\frac{2}{3}} y + x y^{\frac{3}{4}})^{2}

2.66 (u - 6 - 7.17 = 9.83)

24 (2 + 3) 2 - 3

\frac{( x ^{2} + 3 )}{( x + 1 ) ^{2}}

\frac{10 s}{( s + 1 ) ( s + 2 ) ( s + 3 )}

What is expand (9.3+2.1i)^4 ?
The solution to expand (9.3+2.1i)^4 is 5211.4428+6412.0896i