Math Is Fun Forum

gourish

Member

Registered: 2013-05-28

Posts: 153

the imaginary equation of a circle? is that even possible

i read a question saying" if z1 z2 and z3 are the vertices of an equilateral triangle inscribed in a circle mod(z)=3 and z1=1+isqrt(3) what is z2+z3" but the equation of a circle doesn't seem to right (that's what i think but i am not sure) can anybody please explain me is this question even right and is it possible to have such an equation for a circle (in argand plane). i would like a simple explanation which a high school going guy can understand. thanks for the help guys appreciate it.

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"The man was just too bored so he invented maths for fun"
-some wise guy

Bob

Administrator

Registered: 2010-06-20

Posts: 10,144

Re: the imaginary equation of a circle? is that even possible

mod(z) = 3, means a circle with centre (0,0) and radius 3.  z1 certainly lies on such a circle.

If you sketch this, you'll find that the three points are separated by 120 degrees of rotation around (0,0) so that should make it easier to find them.  And adding them.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: the imaginary equation of a circle? is that even possible

well the mod of complex number gives it's distance from the origin of argand plane but the mod of z1 is sqrt(1+3)=2 so it's inside the given circle? or is my concept of modulus of a complex number wrong?

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"The man was just too bored so he invented maths for fun"
-some wise guy

Bob

Administrator

Registered: 2010-06-20

Posts: 10,144

Re: the imaginary equation of a circle? is that even possible

hi gourish,

Oh yes.  I missed that.    Yes the circle should be mod(z) = 2.  Another typo I think. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: the imaginary equation of a circle? is that even possible

thanks bob i was all messed up thinking that the question is just out of my league... but what if the circle was mod(z)=2 what would be the other two vertices z2 and z3?

---

"The man was just too bored so he invented maths for fun"
-some wise guy

Bob

Administrator

Registered: 2010-06-20

Posts: 10,144

Re: the imaginary equation of a circle? is that even possible

z1 is 60 degrees round from the positive x axis, so z2 will be at 180, and z3 at 300.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: the imaginary equation of a circle? is that even possible

oh.. so just using the euler representation for the complex numbers is the simplest approach thanks bob..

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"The man was just too bored so he invented maths for fun"
-some wise guy