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What is the quotient of the complex number  \(4-3i\)  divided by its conjugate?

 May 1, 2021
 #1
avatar+1300 
+1

(4-3i)/(4+3i) = 0.28 - 0.96i

 

=^._.^=

 May 1, 2021
 #2
avatar
+1

Do you know how to convert that into a fraction?

Guest May 1, 2021
 #4
avatar+1300 
+1

Sure, here's another way of doing it. 

(4+3i)(a+bi) = 4-3i

4a-3b + 3ai + 4bi = 4 - 3i

4a-3b = 4

3ai + 4bi = -3i

3a + 4b = -3

4a - 3b = 4

a = 7/25

b = -24/25

 

7/25 - 24/25i

 

=^._.^=

catmg  May 1, 2021
edited by catmg  May 1, 2021
edited by catmg  May 1, 2021
 #3
avatar+113177 
+2

Thanks Catmg, some working might be helpful

 

 

\(\frac{4-3i}{4+3i}\\ =\frac{4-3i}{4+3i}\times \frac{4-3i}{4-3i}\\ =\frac{16-9-24i}{16+9}\\ =\frac{7-24i}{25}\\ \)

 May 1, 2021
 #5
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0

The answer wasn't what cat said? I've been trying to use latex to write my answers down but I can't figure it out.

Guest May 1, 2021
 #6
avatar+1300 
+1

Oops, I def should've added some work.

I'll add my work below since I used a different method. 

 

Melody and I have the same answer, it's just in a different form. :))

 

=^._.^=

catmg  May 1, 2021
 #12
avatar+113177 
+1

Our answers are the same.  catmg just wrote it in decimal form.

Melody  May 1, 2021
 #7
avatar
+2

Thank you catmg and Melody!!! I'm glad you guys actually show me how to get the answer. Some people just write the answer and don't explain it.

 May 1, 2021
 #8
avatar+1300 
+1

You're welcome. :))

Glad you understand. 

Remember that conjugate is just the negative of the imaginary part, so a + bi turns into a - bi. 

 

=^._.^=

catmg  May 1, 2021
 #9
avatar
+1

Gotcha! Thanks!

Guest May 1, 2021
 #13
avatar+113177 
0

If you want more explantion, always ask for it.

 

I mean you can say, "Thanks for the answer but can you show me how you got that please"

 

 

I like it when people ask me questions related to my answer. 

It means I actually have an audience and someone at the other end is actually trying to learn from me.

Melody  May 1, 2021
edited by Melody  May 1, 2021
 #10
avatar+118611 
+2

THX, catmg  and Melody   !!!!

 

We couldn't do without  either of you guys  ( that's OK in Australia   !!!   )

 

 

 

cool cool cool

 May 1, 2021
 #11
avatar+113177 
+2

Thanks Chris,

 

Yep. that is ok in Australia.  Guys, used like this, includes females.   laugh

 

General usage in Australia.

A guy = a male person

guys = A group of people male and/or female.  

Melody  May 1, 2021

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