Complex question (1 Viewer)

[HyperComplexxx]

P represents complex number z and R represents complex number1/z. PQRS is draw with PR as diagonal, if P lies on circle |z| = 2,

i. Prove Q lie on ellipse whose equation has the form


Any help would be appreciated

 

[funnytomato]

P represents complex number z and R represents complex number1/z. PQRS is draw with PR as diagonal, if P lies on circle |z| = 2,

i. Prove Q lie on ellipse whose equation has the form



Any help would be appreciated

did u mean PQRS is a square?

 

[funnytomato]

basically i assumed you meant PQRS is a square coz it's the easiest case..

so P is 2cis(alpha)
R is 1/2(cis -alpha)

let Q = x+iy
since it's a square, vector QP= vector QR*i

solve for x and y
then you can express x and y in terms of sin(alpha) and cos(alpha)
after some algebra, I got a^2=25 , b^2=9 (hopefully they're right, and assumption as well )

 

[HyperComplexxx]

yea sorry it was a square
thanks for help

i got a = and b =