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Homework
Will be discussed in class on Monday.
Week 10
On Monday we showed that to multiply one complex number by another
involves stretching
by a factor of
and then rotating through an angle
. On Tuesday we used this information to find roots of unity. We also spoke about the Conjugate Root Theorem.
Week 11
More on complex numbers including De Moivre’s Theorem and taking roots.
Exercises
For the Week 11 tutorial you should look at Q.54 and 61-63.
Math.Stack Exchange
If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this conjecture about calculating .
2 comments
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March 18, 2014 at 3:57 pm
Student
Hi JP,
I just have a few questions regarding the homework,
When representing the conjugate of a complex number geometrically, is it acceptable to describe it as a rotation by the negative value of the original angle of the equation?
e.g.
implies that
.
If the angle between
and the
-axis is 30 degrees, is the conjugate not just a rotation by -30 degrees as only the value of the imaginary number changes?
For question 1 on the homework is
the product or the composition?
Thanks,
March 18, 2014 at 4:00 pm
J.P. McCarthy
Hi,
A better way of thinking would be to say that the conjugate of
is the reflection of
in the real (
) axis.
If you were doing it using rotations, the conjugate would actually be a rotation of
through an angle
…
Regards,
J.P.