madmerc
  • madmerc
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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  • schrodinger
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madmerc
  • madmerc
@CShrix
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  • madmerc
@Maddy1251 @IHelpYouLearn @Halmos
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  • madmerc
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More answers

LanHikari22
  • LanHikari22
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?
madmerc
  • madmerc
Put both of what together?
LanHikari22
  • LanHikari22
Real, and imaginary numbers. If you want to put both in the same equation, what do you do?
madmerc
  • madmerc
I don't know...
madmerc
  • madmerc
Add them?
LanHikari22
  • LanHikari22
Yeah, pretty much.
LanHikari22
  • LanHikari22
They're not special in that sense, you just add them.
LanHikari22
  • LanHikari22
but you keep in mind that, it's like adding this 5 + 6X. so it's absolutely not 11X. it's just... 5 + 6X
madmerc
  • madmerc
So what am I adding exactly?
LanHikari22
  • LanHikari22
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
LanHikari22
  • LanHikari22
So the result would be an option that add both.
madmerc
  • madmerc
so the answer is just -1 + 3i ?
LanHikari22
  • LanHikari22
yup
madmerc
  • madmerc
thank you! can you help me with another?
LanHikari22
  • LanHikari22
if it's the same thing, it should follow the same methods, though.
LanHikari22
  • LanHikari22
Make sure you understand why, not just how.
madmerc
  • madmerc
It's not it's \[\frac{ \sqrt{-49} }{ (7 - 2i) - (4 + 9i) }\]
madmerc
  • madmerc
I don't remember how to do this and I have to finish a bunch of assignments I missed while I was sick
LanHikari22
  • LanHikari22
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: |dw:1446933581607:dw| 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.
LanHikari22
  • LanHikari22
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!

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