Need help with complex numbers! (i)

[kristopher0123]

Alright so I don't even know how to explain this lol so i'll write what i know. Standard Form: a+bi where a is the "real" component" and bi is the "imaginary part". I don't think 'solving the equations' would be the right word. I guess maybe finding the standard form of it? Anyways... here's where I'm having trouble. I was wondering if 1. a+bi = -a-bi? which leads to my other question...

(5+2i)(2-4i) is what i'm given so...here's my work...
10 - 20i + 4i - 8i^2
10 - 20i + 4i + 8
18 - 16i = standard form

But the standard form is a + bi, so does it need to be -18 + 16i? Or is it correct already? Thanks everyone!

Also on the topic of *does a=-a* or whatever you want to call it...on a different question, I got

(-12/100)(16/100)i

is this the same as (-3/25)(4/25)i ? Thanks!

 

[mmm4444bot]

… Standard Form: a+bi where a is the "real" component" and bi is the "imaginary part" …

This is not correct. The imaginary unit is i.

The imaginary part is b.

The numbers a and b are both Real.

When b = 0, the Complex number a + bi is also the Real number a, and the imaginary part is zero. In other words, not all Complex numbers have an imaginary component.

… I was wondering if … a + bi = -a - bi … Factor out -1 on the righthand side, and you'll see that they are not equal.

… (5+2i)(2-4i) …

… 18 - 16i = standard form Yes, this is correct.

… But the standard form is a + bi … There is no contradiction here.

-16i just shows that b = -16 in the number a + bi.

In a Complex number, either or both the Real numbers a and b may be positive or negative.

MY EDITS: Clarified difference between imaginary unit and imaginary part

 

[kristopher0123]

Thanks lol.
Standard Form: a+bi where a is the "real" component" and bi is the "imaginary part" was copied directly from a text book hahahaha

 

[mmm4444bot]

… The imaginary part is i …

Whoops; I did not type what I was thinking. (I will edit my post above.)

I meant to say that the imaginary part of a Complex number comes from i.

I apologize for any confusion. Let me start over.

A Complex number is any number of the form a + bi .

where i = the imaginary unit

b = the imaginary part of the Complex number

a = the Real part of the Complex number

Note that both the Real and imaginary parts of a Complex number (i.e., a and b) are Real numbers.

So, the imaginary part is not bi, it's simply b.

(Again, the symbol i represents the imaginary unit, not the imaginary part of a Complex number.)

Here's some examples.

6i is a Complex number; it's Real part is zero, and it's imaginary part is 6.

Complex numbers with a Real part of zero (i.e., 0 + bi) are called "pure imaginary numbers".

-7 is a Complex number; it's Real part is -7, and it's imaginary part is zero.

So, all Real numbers are also Complex numbers. (The Real numbers are a subset of the Complex Number System.)

 

[kristopher0123]

Yeah I know what you meant =P thanks for the help lol =) any idea about the second part of my question? =S

does (-12/100)(16/100)i = (-3/25)(4/25)i ?

 

[mmm4444bot]

(-12/100)(16/100)i = (-3/25)(4/25)i

Yes, these two expressions are equal.

(I'm not sure what motivated your question about this equality.)

You also previously typed the following equation:

a = -a

This equation is a statement that some arbitrary Real number equals its own opposite.

Well, this is only true when a = 0 because zero is the only Real number which is neither positive nor negative.

Look at the following number:

a

We have no idea whether or not this number is positive or negative. (Only after we have some value(s) for a, will we know for sure.)

Look at the following number:

-a

Again, we have no idea whether or not this number is positive or negative. (Only after we have some value(s) for a, will we know for sure.)

Without knowing any value(s) for a, the only thing that we can be sure of is that a does not equal -a (except for the single case when a = 0).

 

[kristopher0123]

Yeah I know, I didn't know how else to explain it lol. Thanks though!