|z-3i|=5

Lösung

∣ z - 3 i ∣ = 5

z = x + (3 + - x^{2} + 25) i, z = x + (3 - - x^{2} + 25) i; x \in R

Schritte zur Lösung

∣ z - 3 i ∣ = 5

Ersetze

z = x + y i

∣ x + y i - 3 i ∣ = 5

Schreibe

∣ x + y i - 3 i ∣

um:

x^{2} + y^{2} - 6 y + 9

x^{2} + y^{2} - 6 y + 9 = 5

Löse nach

y : y = 3 + - x^{2} + 25, y = 3 - - x^{2} + 25

Setze in

z = x + y i

ein

z = x + (3 + - x^{2} + 25) i, z = x + (3 - - x^{2} + 25) i; x \in R

y = in (2 x), y, y = 1, y = 6

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

y i n^{0} = 3 y^{2} + x - 1

\frac{s i}{P ( x )} = (x - 1)^{2} + x - 1

(z - \frac{3}{5})^{2} + (5 i)^{2} = 0