What is the answer to i(p)=3500-24p^2 ?

The answer to i(p)=3500-24p^2 is p=(sqrt(335999))/(48)-1/48 i,p=-(sqrt(335999))/(48)-1/48 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

i(p)=3500-24p^2

i (p) = 3500 - 24 p^{2}

p = \frac{335999}{48} - \frac{1}{48} i, p = - \frac{335999}{48} - \frac{1}{48} i

Solution steps

i (p) = 3500 - 24 p^{2}

Substitute

p = x + y i

i (x + y i) = 3500 - 24 (x + y i)^{2}

Expand

- y + i x = (3500 - 24 x^{2} + 24 y^{2}) - 48 i x y

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

[- y = 3500 - 24 x^{2} + 24 y^{2} x = - 48 x y]

[- y = 3500 - 24 x^{2} + 24 y^{2} x = - 48 x y] : (x = \frac{335999}{48}, x = - \frac{335999}{48}, y = - \frac{1}{48} y = - \frac{1}{48})

Substitute back

p = x + y i

p = \frac{335999}{48} - \frac{1}{48} i, p = - \frac{335999}{48} - \frac{1}{48} i

E, x = \frac{R}{R + E} i (E)

x, x^{2} - y^{2} i f x = - 3

(m - \frac{1}{2}) (m - 3 - i) = 0

x, y = - x^{2} + 1 g r a f i c a r

z^{2} + 4 i = 0

What is the answer to i(p)=3500-24p^2 ?
The answer to i(p)=3500-24p^2 is p=(sqrt(335999))/(48)-1/48 i,p=-(sqrt(335999))/(48)-1/48 i