Re (iz)/Im(z quer)
Re(i·z) = Re(i·(x + i·y)) = Re(i·x + i^2·y) = Re(i·x - y) = - y
Im(z quer) = Im(x - i·y) = - y
Re(...)/Im(...) = - y / - y = 1
Re((1 - i) * z) - Im((1 - i) * z quer)
Re((1 - i) * (x + i·y)) - Im((1 - i) * (x - i·y))
Re(- i·x + x - i^2·y + i·y) - Im(- i·x + x + i^2·y - i·y)
Re(- i·x + x + y + i·y) - Im(- i·x + x - y - i·y)
(x + y) - (-x - y)
2·x + 2·y
i·z^2 + 4·z - 3 = 0
i·(x + i·y)^2 + 4·(x + i·y) - 3 = 0
i·(x^2 + 2·i·x·y + i^2·y^2) + (4·x + 4·i·y) - 3 = 0
i·(x^2 + 2·i·x·y - y^2) + (4·x + 4·i·y) - 3 = 0
(i·x^2 + 2·i^2·x·y - i·y^2) + (4·x + 4·i·y) - 3 = 0
(i·x^2 - 2·x·y - i·y^2) + (4·x + 4·i·y) - 3 = 0
i·x^2 - 2·x·y + 4·x - i·y^2 + 4·i·y - 3 = 0
Realteil
- 2·x·y + 4·x - 3 = 0
y = (4·x - 3)/(2·x)
Imaginärteil
x^2 - y^2 + 4·y = 0
x^2 - ((4·x - 3)/(2·x))^2 + 4·((4·x - 3)/(2·x)) = 0
x^2 - (4·x - 3)^2/(4·x^2) + (8·x - 6)/x = 0
(4·x^4 + 16·x^2 - 9)/(4·x^2) = 0
4·x^4 + 16·x^2 - 9 = 0
x = - √2/2 --> y = (4·(- √2/2) - 3)/(2·(- √2/2)) = 3·√2/2 + 2
x = √2/2 --> y = (4·(√2/2) - 3)/(2·(√2/2)) = 2 - 3·√2/2
√(-7) = √7·i
√i = √2/2 + √2/2·i
√(4 + 3·i) = 3·√2/2 + √2/2·i