Question

Which of the following is the conjugate of a complex number with –1 as the real part and 3i as the imaginary part?

-1 - 3i
-1 + 3i
-3i + 1
3i + 1

Answer 1

@CShrix

Answer 2

@Maddy1251 @IHelpYouLearn @Halmos

Answer 3

@Nnesha @baru @freckles @AlexandervonHumboldt2 @katragaddasaichandra

Answer 4

You know how to write real numbers, right?
5, 2, 12.23323.
You know how to write complex numbers too, right?
A complex number must contain an imaginary part in it. or in other words, a negative square root!
sqrt(-4) is the same as sqrt(-1 * 4) so we just right it as i*sqrt(4) because
i = sqrt (-1) and square roots can be broken like:
sqrt(2) * sqrt(2) = sqrt(4) = 2.
so sqrt(-4) = sqrt(-1) * sqrt(4) = 2i.
So how do we put both together, now?

Answer 5

Put both of what together?

Answer 6

Real, and imaginary numbers. If you want to put both in the same equation, what do you do?

Answer 7

I don't know...

Answer 8

Add them?

Answer 9

Yeah, pretty much.

Answer 10

They're not special in that sense, you just add them.

Answer 11

but you keep in mind that, it's like adding this
5 + 6X. so it's absolutely not 11X. it's just... 5 + 6X

Answer 12

So what am I adding exactly?

Answer 13

Or 6(1 + X) if you've got things like 6 + 6X, but you can't break your ordinary algebra rules.
Your question here is asking which of the choices has a real number -1, and a complex number 3i

Answer 14

So the result would be an option that add both.

Answer 15

so the answer is just -1 + 3i ?

Answer 16

yup

Answer 17

thank you! can you help me with another?

Answer 18

if it's the same thing, it should follow the same methods, though.

Answer 19

Make sure you understand why, not just how.

Answer 20

It's not it's \[\frac{ \sqrt{-49} }{ (7 - 2i) - (4 + 9i) }\]

Answer 21

I don't remember how to do this and I have to finish a bunch of assignments I missed while I was sick

Answer 22

Alright, I'm going to give you the rules. As well as how negative products work.
Consider this table, which you might've seen already:
i^1 = sqrt(-1)
i^2 = -1
i^3 = -i
i^4 = 1
Normal intuition would say i^2 = 1, because sqrt(-1) * sqrt(-1) = sqrt(--1) = sqrt(1), right?
But, the one thing you need to keep in mind is that INSIDE RADICALS, NEGATIVE/POSITIVE MULTIPLICATION IS NOT -- = +
it's because of this:

Basically, inside radicals, negative sign multiplication works 90 degrees instead of 180, which is - to + to - to +
sqrt(-) = comes out as i
sqrt(--) = sqrt(-^2) you can think of it, and it comes out as... yeah -. or -1
sqrt(---) = sqrt(-^3) = sqrt(-^2 * -) = -sqrt(-) = -i
sqrt(----) = sqrt(-^4) = -^2 = -1 * -1 = +1
This should allow you to multiply complex numbers as you want, everything now is according to the normal laws of algebra you use.

Answer 23

Now, for your problem, you can consider i = X, and simplify, while keeping the sign multiplication in mind if needed. In your problem, it's not needed. sqrt(-49) simplifies to norma 7i, so. Good luck!