What is the answer to (1+isqrt(3))^{11}=a+ib ?

The answer to (1+isqrt(3))^{11}=a+ib is a=1024,b=-1024sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1+isqrt(3))^{11}=a+ib

(1 + i 3)^{11} = a + ib

a = 1024, b = - 10243

Solution steps

(1 + i 3)^{11} = a + ib

Expand

(1 + i 3)^{11} : 1024 - 10243 i

1024 - 10243 i = a + ib

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[1024 = a - 10243 = b]

[1024 = a - 10243 = b] : a = 1024, b = - 10243

a = 1024, b = - 10243

a + bi + 0 + 0 i = a + bi

x, f i = \frac{g r}{x}

z^{2} - (5 - 4 i) z + 20 i = 0

x + i y - 2 i - 3 = x + i y + 2 i + 3

∣ z ∣^{2} + z - i = 11

What is the answer to (1+isqrt(3))^{11}=a+ib ?
The answer to (1+isqrt(3))^{11}=a+ib is a=1024,b=-1024sqrt(3)