Let G = { a + bi | I a + bi I ≤ 4 } Which of the following are in G. (a) 3 + 3i (b) 3i (c) -4 + 3i (d) i^5 (e) 4 - 4i (f) 6 + 2i

Question

Let G = { a + bi | I a + bi I ≤ 4 } Which of the following are in G.  (a) 3 + 3i (b) 3i (c) -4 + 3i (d) i^5 (e) 4 - 4i (f) 6 + 2i

anonymous · Answer

I swear I would not be asking if I knew how to do it. I'm not being lazy I have no clue :( My teacher is lazy

kinggeorge · Answer

Well, to find out, all you have to do is find if$$\sqrt{a^2+b^2} \leq 4$$In other words, $$a^2+b^2 \leq 16$$

kinggeorge · Answer

Also, $i^5=i$ if you didn't know.

kinggeorge · Answer

By my calculations, b and d should be in G, but the rest aren't.

anonymous · Answer

Thank you very much but how do you find out what should be in there

kinggeorge · Answer

By the formula I posted above. All the numbers are of the form $a+bi$ for some $a, b \in \mathbb{R} $  so then you just use the formula I wrote above.

anonymous · Answer

Hmm shouldn't that mean a should be in there as well 3 + 3i = 3 + √-9 ≤ 16?

kinggeorge · Answer

No, since $a=b=3$ so $3^2+3^2=18$ and this is not less than 16.

kinggeorge · Answer

Remember you need to square the numbers and then add them.

anonymous · Answer

Right, I'm an idiot lol thank you very much

kinggeorge · Answer

You're welcome.