Question

Prove that all values of 〖(1-i) 〗^(i√2) lie on a straight line. Were i is the imaginary number √(-1).

Answer 1

is that\[\large (1-i)^{i\sqrt{2}}\]?

Answer 2

Yes

Answer 3

upon simplification, we get
\[ \huge \left( \sqrt{2} e^{i\pi\over 4}\right )^{i\sqrt2}\]
using this probably you will find the principle root.

Answer 4

do you need to find all the roots?

Answer 5

Yes please

Answer 6

I don't know right now ... let me ask some other people. most likely I'm thinking ... it has only one root.

Answer 7

Thank you. I will post another problem in complex analysis.

Answer 8

\[ \huge \left( e^{\ln \sqrt2+{i\pi\over 4}}\right )^{i\sqrt2} = e^{{-\sqrt 2 \over 4} + i\sqrt 2 \ln 2}\]

Answer 9

Many Thanks

Answer 10

no probs ...hardly i put any effort.