find the principle value of

the modulus of (-i)^2+i

You mean the principle value of the argument?
Yes. >>1 was stated badly, ignore it. I need to solve >>4

I've almost got it

(1-i) = \sqrt2e^{-4/\pi}

Principle value is ln(\sqrt2) {-i\pi/4}

So |(1-i)^{2i-1}|=|e^{(ln(\sqrt2)-i\pi/4)(2i-1)} |

|(1-i)^{2i-1}|=|e^{(2iln\sqrt2 +\pi/2-ln\sqrt2+i\pi/4} |

Anyone know how to tidy up the last term so it's not in exponential form?