What is the answer to z-1/z =3+3i ?

The answer to z-1/z =3+3i is z=-0.17477…+0.15653…i,z=3.17477…+2.84346…i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

z-1/z =3+3i

z - \frac{1}{z} = 3 + 3 i

z = - 0.17477 \dots + 0.15653 \dots i, z = 3.17477 \dots + 2.84346 \dots i

Solution steps

z - \frac{1}{z} = 3 + 3 i

Substitute

z = x + y i

x + y i - \frac{1}{x + y i} = 3 + 3 i

Multiply both sides by

x + y i

x (x + y i) + y i (x + y i) - \frac{1}{x + y i} (x + y i) = 3 (x + y i) + 3 i (x + y i)

Expand

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

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

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

[x^{2} - y^{2} - 1 = 3 x - 3 y 2 x y = 3 x + 3 y] : (x = - 0.17477 \dots, x = 3.17477 \dots, y = 0.15653 \dots y = 2.84346 \dots)

Substitute back

z = x + y i

z = - 0.17477 \dots + 0.15653 \dots i, z = 3.17477 \dots + 2.84346 \dots i

x^{2} + (i - 10) x + 23 - 11 i = 0

i (x) = 2000 x - 2 x^{2}

r = \frac{v}{i}

z^{2} (3 - i) + 5 (1 - i) z + 2 + 16 i = 0

z^{2} = - 5 + i

What is the answer to z-1/z =3+3i ?
The answer to z-1/z =3+3i is z=-0.17477…+0.15653…i,z=3.17477…+2.84346…i