en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (4+3i)^5

Solution

simplify

(4 + 3 i)^{5}

Solution

- 3116 - 237 i

Solution steps

(4 + 3 i)^{5}

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 5 (i 5) \cdot 4^{(5 - i)} (3 i)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 4^{5} (3 i)^{0} : 1024

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 4^{4} (3 i)^{1} : 3840 i

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 4^{3} (3 i)^{2} : 5760 i^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 4^{2} (3 i)^{3} : 4320 i^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 4^{1} (3 i)^{4} : 1620 i^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 4^{0} (3 i)^{5} : 243 i^{5}

= 1024 + 3840 i + 5760 i^{2} + 4320 i^{3} + 1620 i^{4} + 243 i^{5}

Simplify

1024 + 3840 i + 5760 i^{2} + 4320 i^{3} + 1620 i^{4} + 243 i^{5} : - 237 i - 3116

= - 237 i - 3116

Rewrite in standard complex form:

- 3116 - 237 i

= - 3116 - 237 i

Popular Examples

expand ((6x-5)^2)/(36)expand

\frac{( 6 x - 5 ) ^{2}}{36}

expand (1/(p^2)-4q)^7 expand

(\frac{1}{p ^{2}} - 4 q)^{7}

simplify (x^2+4i)^2 simplify

(x^{2} + 4 i)^{2}

simplify (1+cos(x))(cos(x))simplify

(1 + cos (x)) (cos (x))

expand 1-sin(x)(1+sin(x))expand

1 - sin (x) (1 + sin (x))

Frequently Asked Questions (FAQ)

What is (4+3i)^5 ?
The solution to (4+3i)^5 is -3116-237i