What is the answer to z*z+z=3-i ?

The answer to z*z+z=3-i is z=1.32350…-0.27419…i,z=-2.32350…+0.27419…i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

z*z+z=3-i

z \cdot z + z = 3 - i

z = 1.32350 \dots - 0.27419 \dots i, z = - 2.32350 \dots + 0.27419 \dots i

Solution steps

zz + z = 3 - i

Substitute

z = x + y i

(x + y i) (x + y i) + x + y i = 3 - i

Simplify

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

(x^{2} - y^{2} + x) + i (y + 2 x y) = 3 - i

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

[x^{2} - y^{2} + x = 3 y + 2 x y = - 1]

[x^{2} - y^{2} + x = 3 y + 2 x y = - 1] : (x = 1.32350 \dots, x = - 2.32350 \dots, y = - 0.27419 \dots y = 0.27419 \dots)

Substitute back

z = x + y i

z = 1.32350 \dots - 0.27419 \dots i, z = - 2.32350 \dots + 0.27419 \dots i

a + bi = - i

x + 2 i = 5 + y i

x^{2} + i x 3 + i = 0

3 x^{2} + (1 - i) x + 3 i = 0

x^{2} + (4 - 2 i) x - (1 + i) = 0

What is the answer to z*z+z=3-i ?
The answer to z*z+z=3-i is z=1.32350…-0.27419…i,z=-2.32350…+0.27419…i