Question

em cada caso determine z €C
b)z^2=2i

Answer 1

z=a+bi

z²=(a+bi)²=a²+2abi+b²i²

z²=a²+2abi+b²(-1)

z²=a²-b²+2abi

Z²=2i

z²=0+2i

a²-b²+2abi=0+2i

{a²-b²=0

{2abi=2i

2ab=2

ab=1

{a²-b²=0

{ab=1 →a=1/b

(1/b)²-b²=0

1/b² - b²=0

1-b⁴=0

b⁴=1

b=∜1

b=1

ab=1

a.1=1

a=1