Radius of a circle in complex numbers

[south stone]

I tried something but I actually am really weak in this topic and I would like to know a good method to solve it

[south stone]

This is what I tried

I have to study many topics too so if you'd like to help then ping me, I might come

[slow knoll]

Whenever you deal with complex fraction, we try to decomplexify the deniminator. We do this by extending the fraction by the conjugate of the denominator

[south stone]

Okay

[slow knoll]

What is the conjugate of z + 3i?

[south stone]

Z - 3i

[slow knoll]

yes

[south stone]

Z will become z bar?

[slow knoll]

this is what you multiply numerator and denominator by

[slow knoll]

Yes

[south stone]

x - (3+y)i

They have given z to be x + iy

[slow knoll]

Yes

[south stone]

Yes I got it

Yes

[hard crystal]

adonhs

[south stone]

Yes

[slow knoll]

Did you get the answer?

[south stone]

No

[slow knoll]

Ok

[south stone]

There was a similar question that I saw

But the last few steps blew over my head

[slow knoll]

Actually it was a good step of yours to multiply by the denominator

[south stone]

No I just followed some standard similar question

[slow knoll]

Now write z = x+iy

[south stone]

Done

[hard crystal]

adonhs

[slow knoll]

Now the trick is to factor i

And use the definition of modulus

[south stone]

You mean x + (y-1)i

[slow knoll]

YES

[south stone]

Oh

And zzbar is mod z square

[hard crystal]

adonhs

[south stone]

That's why it broke up

[slow knoll]

Now you know the imaginary part and real part to use modulus

[hard crystal]

adonhs

[south stone]

Oh this definition

[slow knoll]

Now try to simplify

[south stone]

I'll get ±

[south stone]

Could you please explain this method too

Uhh

@slow knoll?

What

[hard crystal]

adonhs

[slow knoll]

Have you never heard of complex modulus

[south stone]

I have

[slow knoll]

To get the radius basically

[south stone]

What do I do now

[slow knoll]

Try to get this form:

x² + y² = r²

So for y you need to complete the square

Also there is no +-

The root value is always positive

I also think you simplified wrong

49 remains

It's not included in the root

It'sbasically outside the absolute value

[south stone]

Its very lengthy

[slow knoll]

6x² + 6y² + 37y = -55

[south stone]

What

[slow knoll]

If you complete the square for y, you will get radius 7/12

And make it a circle equation

[hard crystal]

adonhs

[south stone]

So I divide by 6

[slow knoll]

Yea

I hope you know how to complete the square

[south stone]

To be honest

I kind of forgot

💀

You add and subtract 37/12 both sides

Idk something like that

[slow knoll]

almost

(37/12)²*

Then (37/12)²-55/6

[south stone]

Oh you square it

[slow knoll]

Is your r²

[slow knoll]

Yes

basically if a² + 2ab + b², you dont do b you do b²

for example

[south stone]

Yeah

[slow knoll]

,w r^2 = (37/12)^2 - 55/6

[south stone]

I got 49/144

[hard crystal]

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Requested by adoniszgks

[south stone]

Yup

7/12

Thank you so much!!!

[slow knoll]

If you get the hang it's easy basically

5 to 10min max

[south stone]

Yeah

Well uh

Time is the problem, that's kind of...

[jaunty plover]

If you are done with this channel, please mark your problem as solved by typing .close

[south stone]

.close

[jaunty plover]

Solved

Post marked as solved by @south stone.

Use .unsolved if this was a mistake.

[slow knoll]

What is that

[south stone]

The syllabus

Exams tomorrow

30 mins for 30 questions

[slow knoll]

Such a question in 1 min?

[south stone]

So 5-10 mins for single question would be more harm than good

[south stone]

We have easy ones too

[slow knoll]

Ok maybe there is another approach

For this

[south stone]

See this is easy

@slow knoll maybe this approach

I tried it

It was very bad

[hard crystal]

adonhs

[slow knoll]

You're prob right lmao

[south stone]

Lmao

[south stone]

I just don't know what they did here

[slow knoll]

Maybe there a shortcuts

[hard crystal]

adonhs

[slow knoll]

Since you have |z-1|²

[slow knoll]

You can rewrite it using this

[south stone]

Yes

[slow knoll]

But thats also my first time seeing such circle equation in that form

[south stone]

Same

They used g and f

,help

[hard crystal]

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[south stone]

$x^2$

[hard crystal]

Rage123

[south stone]

$x^2 + y^2 + 2gx + 2fy + c = 0$

[hard crystal]

Rage123

[south stone]

This equation

They used this