Complex Numbers: u = i^5z is found by...
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Complex Numbers: u = i^5z is found by...

[From: ] [author: ] [Date: 13-05-28] [Hit: ]
therefore,Im really unsure, and I would really appreciate if someone could explain this to me. Also, Im required to explain why all of the other options are wrong, and Im a bit lost for how to do that.......
A: reflecting z in the Im(z) axis
B: reflecting z in the Re(z) axis
C: reflecting z in the line Im(z) = Re(z)
D: rotating z through π/2 about the origin (i.e. anticlockwise)
E: rotating z through - π/2 about the origin (i.e. clockwise)

I'm fairly certain it is D, because the axis have swapped?
i5 = i
therefore, u = xi - y

I'm really unsure, and I would really appreciate if someone could explain this to me. Also, I'm required to explain why all of the other options are wrong, and I'm a bit lost for how to do that.

Help appreciated

-
As you say, u=iz and this rotates the line O to point z anticlockwise
through π/2.
If you express z by x+iy with point P having coordinates (x,y)
then iz = i(x+iy) = -y+ix and this has coordinates (-y, x) and from
a diagram you can see that it rotates OP anticlockwise through π/2.

The axes have not been swapped, that would imply a reflection in the
line y=x.

You can show that an option is wrong by choosing a particular point
consistent with that option but not with the correct option.e.g.
A. if z=1then u=iz=i but u is clearly not a reflection of z in Im(z).
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