What is the answer to 2z^2-5iz-2z=0 ?

The answer to 2z^2-5iz-2z=0 is z=0,z=1+5/2 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2z^2-5iz-2z=0

2 z^{2} - 5 i z - 2 z = 0

z = 0, z = 1 + \frac{5}{2} i

Solution steps

2 z^{2} - 5 i z - 2 z = 0

Substitute

z = x + y i

2 (x + y i)^{2} - 5 i (x + y i) - 2 (x + y i) = 0

Expand

2 (x + y i)^{2} - 5 i (x + y i) - 2 (x + y i) : (2 x^{2} - 2 y^{2} + 5 y - 2 x) + i (- 2 y - 5 x + 4 x y)

(2 x^{2} - 2 y^{2} + 5 y - 2 x) + i (- 2 y - 5 x + 4 x y) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(2 x^{2} - 2 y^{2} + 5 y - 2 x) + i (- 2 y - 5 x + 4 x y) = 0 + 0 i

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

[2 x^{2} - 2 y^{2} + 5 y - 2 x = 0 - 2 y - 5 x + 4 x y = 0]

[2 x^{2} - 2 y^{2} + 5 y - 2 x = 0 - 2 y - 5 x + 4 x y = 0] : (x = 0, x = 1, y = 0 y = \frac{5}{2})

Substitute back

z = x + y i

z = 0, z = 1 + \frac{5}{2} i

(2 x + y) + (3 i - 5 x i) = 1 - 7 i

0.005 x i = \frac{1}{0.000018 x i}

z^{2} - (3 + 6 i) z - 4 - 6 i = 0

i (x + i y) = x + i + i 2 y

4 - i x = y - 3 i

What is the answer to 2z^2-5iz-2z=0 ?
The answer to 2z^2-5iz-2z=0 is z=0,z=1+5/2 i