complex no. (1 Viewer)

[juantheron]

 

[iEatOysters]

Do you have the answer? I think I got it... But I think it's wrong.

 

[wagig]

My answer's root 2 haha, let me know if it's right and i'll show how i got it

 

[rumbleroar]

I got root 2 as well

 

[HeroicPandas]

Did u guys use circle geometry (with root of unity) and pythagoras?

 

[rumbleroar]

^ Yea pretty much
I think you can also use isosceles triangles?

 

[HeroicPandas]

^ Yea pretty much
I think you can also use isosceles triangles?

ok cool, yeh i used isos triangle too

 

[wagig]

I did it a weird way i'm pretty sure,
I used vectors, cos rule () and algebra manipulation

 

[blootomarto]

What is the method of solving this?

 

[braintic]

There is something wrong with this question.

Let z1=1, z2=1, z3=-1.
These satisfy the first requirement that they all have unit modulus.

So it satisfies the second requirement.


Now let z1=1, z2=i, z3=i.
Again the two requirements are met (you can check), but this time the answer is sqrt 2.

In fact I made a Geogebra construction, and you can get an infinite number of answers.

I think the question might be correct if you had asked for the MAXIMUM value of

 

[Drongoski]

0 < |z₁ + z₃| < 2 ??

 

[cineti970128]

What is the method of solving this?

Draw a circle with three point A, B, C representing z1, z2, z3.
By inspecting the formula, angle at A is 90. Hence using the semi circle angle property, BC must be a diameter through the origin.
Since z1 can b anywhere, so by inspecting the modulus |z1+z3| formed by adding z1 and z3 , hence > 0 and <2. I don't know how others got root 2.

 

[dunjaaa]

Yeah I got the same ^

 

[Triage]

There is something wrong with this question.

Let z1=1, z2=1, z3=-1.
These satisfy the first requirement that they all have unit modulus.

So it satisfies the second requirement.


Now let z1=1, z2=i, z3=i.
Again the two requirements are met (you can check), but this time the answer is sqrt 2.

In fact I made a Geogebra construction, and you can get an infinite number of answers.

I think the question might be correct if you had asked for the MAXIMUM value of

|z1 - z2| doesn't equal |z1|-|z2|. I don't think something is wrong with the question.

 

[RealiseNothing]

|z1 - z2| doesn't equal |z1|-|z2|. I don't think something is wrong with the question.

I don't see where he has used this?

 

[Triage]

I don't see where he has used this?

|z1-z2|^2 = |1-1|^2

I think that is a nonsense regardless

 

[RealiseNothing]

|z1-z2|^2 = |1-1|^2

I think that is a nonsense regardless

Nah everything he did was correct.

 

[braintic]

|z1-z2|^2 = |1-1|^2

I think that is a nonsense regardless

Not sure what it is you don't get, but all I've done is replace z1 by 1 and z2 by 1. Simple substitution. If you think year 7 substitution is nonsense, well ... what can I say.

Perhaps you could show me where I said that |z1 - z2| equals |z1|-|z2| .

And 'nonsense' is a non-countable noun, so it can't be preceded by 'a' unless you want to use it as an adjective for a countable noun.

 

[Triage]

Not sure what it is you don't get, but all I've done is replace z1 by 1 and z2 by 1. Simple substitution. If you think year 7 substitution is nonsense, well ... what can I say.

Perhaps you could show me where I said that |z1 - z2| equals |z1|-|z2| .

And 'nonsense' is a non-countable noun, so it can't be preceded by 'a' unless you want to use it as an adjective for a countable noun.

Sorry, my bad, I overlooked the substitution and thought you were just substituting in the modulus of z1 and z2. Seriously honest mistake of mine, nt trying to attack you in any way.

 

[alficio]

Draw a circle with three point A, B, C representing z1, z2, z3.
By inspecting the formula, angle at A is 90. Hence using the semi circle angle property, BC must be a diameter through the origin.
Since z1 can b anywhere, so by inspecting the modulus |z1+z3| formed by adding z1 and z3 , hence > 0 and <2. I don't know how others got root 2.

Just wondering isn't it possible that A isn't 90 degrees?