Question

Show that 1) square root of i = 1+i/square root of 2
2) square root of -i = 1-i/square root of 2
Please help me!! Thanks you all! :-)

Answer 1

lets start step by step
1. assume the square root to be a + ib
the (a + ib)^2 = i

now compare the real and imaginary parts and tell me what you get

Answer 2

wait!

Answer 3

I have no idea!
:P

Answer 4

ok
(a + ib)^2 = a^2 + (ib) ^ 2 + 2a(ib) = a^2 -b^2 + 2abi = i

so comparing we get
a^2 - b^2 = 0 and 2ab = 1

now can you solve for a and b?

Answer 5

did you manage to get hold of something?