What is the answer to (1+i)z^2=-1+7i ?

The answer to (1+i)z^2=-1+7i is z=2+i,z=-2-i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1+i)z^2=-1+7i

(1 + i) z^{2} = - 1 + 7 i

z = 2 + i, z = - 2 - i

Solution steps

(1 + i) z^{2} = - 1 + 7 i

Substitute

z = x + y i

(1 + i) (x + y i)^{2} = - 1 + 7 i

Expand

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

(x^{2} - y^{2} - 2 x y) + i (x^{2} - y^{2} + 2 x y) = - 1 + 7 i

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

[x^{2} - y^{2} - 2 x y = - 1 x^{2} - y^{2} + 2 x y = 7]

[x^{2} - y^{2} - 2 x y = - 1 x^{2} - y^{2} + 2 x y = 7] : (x = 2, x = - 2, y = 1 y = - 1)

Substitute back

z = x + y i

z = 2 + i, z = - 2 - i

5 + bi = (a + b i^{2})

z, (2 - i) z + 8 z^{2} = 0

(4 + i) x + (9 - 2 i) y = - 57 + 24 i

x 2 x - 4 y i = 10 - 5 i

z, w = \frac{1}{z + i}

What is the answer to (1+i)z^2=-1+7i ?
The answer to (1+i)z^2=-1+7i is z=2+i,z=-2-i