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

May 1, 2021

#1
+1300
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(4-3i)/(4+3i) = 0.28 - 0.96i

=^._.^=

May 1, 2021
#2
+1

Do you know how to convert that into a fraction?

Guest May 1, 2021
#4
+1300
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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
+113177
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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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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
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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
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Our answers are the same.  catmg just wrote it in decimal form.

Melody  May 1, 2021
#7
+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
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You're welcome. :))

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

=^._.^=

catmg  May 1, 2021
#9
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Gotcha! Thanks!

Guest May 1, 2021
#13
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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
+118611
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THX, catmg  and Melody   !!!!

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

May 1, 2021
#11
+113177
+2

Thanks Chris,

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

General usage in Australia.

A guy = a male person

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

Melody  May 1, 2021