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November 25th, 2009, 10:14 PM   #1
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Complex numbers questions

So I missed the last week of class because I've been sick and with my textbooks stuck in my school lockers, I can't really get caught up on work. My friend was able to send me two sample questions they've been learning in class, but I have no idea what it means? Can someone please explain and teach me how to solve these questions?

Unsure of the notation too, the second z in the first question has a line over it, I don't think it's supposed to be z hat, but that's all I know.

1) Find the complex number z such that .


2) If and are complex numbers, calculate the modulus of .


(Also, is modulus supposed to be like the programming modulus operation, or is it related? (i.e. 15 mod 10 = 5))

Thanks a lot, guys!
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November 26th, 2009, 04:06 AM   #2
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How much complex numbers stuff do you know already?

is the complex conjugate of sometimes written (or rarely ).

It represents the unique complex number satisfying

In other words, if where then

It is a useful exercise (i.e. you should do this ) to check directly that the complex conjugate satisfies the following properties for



The modulus (which is different to the modulo), otherwise known as the absolute value, is then defined to be the unique real, non-negative number satisfying

This means that if then You should check this, too.

The modulus satisfies the following properties for among others:



You should check these, too - most are easy when you express in terms of and and use the properties of the conjugate. I'll show you how to do the triangle inequality one, since this is probably the trickiest:



Therefore


Use the properties of the modulus and conjugate to have a go at your problems, and then come back if you have any further questions!
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