Question

if z^2=-i then is it true that z=+-1/sqrt2(1-i)

Answer 1

If z = (1+i)/√2

Then z can be represented in Euler's form as

Z= e^(i(π/4) )

So this means that z^ 1929 can be written as e^(i(482π+π/4))

=> Z= e^(i(π/4) ) because these functions are periodic with 2π

So z ^1929 =(1+ i)/√2

i hope it helps ☺️