How do I compute the modulus and argument of each complex number?
1+i

Question

How do I compute the modulus and argument of each complex number?
1+i

psymon · Answer

Well, the polar form of a complex number is:
$$r(\cos \theta + isin \theta)$$r is the modulus and theta is the argument. Now we just need to get what you have into the polar form. So we need to be aware of the conversions we have:
$$r ^{2}= a ^{2} + b ^{2}$$
$$\tan \theta = \frac{ b }{ a }$$
$$y = rsin \theta $$
$$x = rcos \theta  $$
These are the main conversions. For going from rectangular to polar, we need the top two. So a complex number is in the form of a + bi. So for you, a = 1 and b also = 1 (because we do not include the i). This make sense so far?

anonymous · Answer

okay so I would do this 1^2+1^2=2?

psymon · Answer

Right. so r^2 = 2, meaning r = sqrt(2)

anonymous · Answer

oh yeah! Almost forgot to square it! And would that be the answer?

psymon · Answer

That'd just be r, which is the modulus. Now we need the argument, which is theta. So for that we need to usethe 2nd conversion listed. So b/a is just 1, right? So where is tan(theta) = 1?