Question

Write the expression as a complex number in standard form 7 over 3 + i

Answer 1

Multiply top and bottom by conjugate? I'm assuming you mean make the denominator real when you say standard form.

Answer 2

Yeah I guess, I really do not get it at all

Answer 3

Are you familiar with complex conjugates?

Answer 4

no, not at all

Answer 5

Ok, the idea is this: if you have a complex number in the form a+bi, when you multiply it by a-bi, you get a real number. Try it for yourself.

Answer 6

alright

Answer 7

If you're not convinced, ask me and I'll show you.

Answer 8

in fact you should just remember that
\[(a+bi)(a-bi)=a^2+b^2\] because it comes up quite frequently

Answer 9

I feel stupid but I do not get it at all

Answer 10

Don't worry.\[(a+bi)(a-bi)=a^2+abi-abi-b^2i^2=a^2-b^2i^2=a^2-b^2\times(-1)=a^2+b^2\]Is that clearer?

Answer 11

I don't know which number represents each letter

Answer 12

That doesn't matter at the moment. All I'm saying is that it works for any a and b.