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

The answer to |z|+z-z*z=3+3i is z=1.60031…-1.36324…i,z=-0.51078…+1.48399…i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|z|+z-z*z=3+3i

∣ z ∣ + z - z \cdot z = 3 + 3 i

z = 1.60031 \dots - 1.36324 \dots i, z = - 0.51078 \dots + 1.48399 \dots i

Solution steps

∣ z ∣ + z - zz = 3 + 3 i

Substitute

z = x + y i

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

Expand

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

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

[x^{2} + y^{2} + x - x^{2} + y^{2} = 3 y - 2 x y = 3] : (x = 1.60031 \dots, x = - 0.51078 \dots, y = - 1.36324 \dots y = 1.48399 \dots)

Substitute back

z = x + y i

z = 1.60031 \dots - 1.36324 \dots i, z = - 0.51078 \dots + 1.48399 \dots i

6 x + 12 y i = (2 x - 3) + (2 y + 3) i

15 + 2 3 x = - 5 x + 2

x^{2} = - 3 i

3 x + 2 x i - 3 y i + 2 y = 0

p = 4 πi r^{2}

What is the answer to |z|+z-z*z=3+3i ?
The answer to |z|+z-z*z=3+3i is z=1.60031…-1.36324…i,z=-0.51078…+1.48399…i