Ext maths 2, complex number question, HELP!!!! (1 Viewer)

[So-smart]

Hi,
I have a ext maths 2 assignment and i am stuck on this complex number question, please help.
I would really appreciate it if you wrote the working out!!
FOREVER GRATEFUL!!!!!

Sketch the locus of those points z such that:

Im (z^2) (greater than or equal to) 1

 

[ronnknee]

Let z = x + iy
z^2 = (x + iy)^2
= x^2 - y^2 + 2xyi

Im (z^2) = 2xy
Therefore Im (z^2) >= 1
2xy >= 1
xy >= 1/2
y >= 1/2x

This is the locus of a hyperbola where P(1/4, 2) lies on it, with the area outside the hyperbola (away from the axes) are shaded


Contact me if you're interested in tutoring

http://community.boredofstudies.org...r-11-12-math-2u-3u-4u-around-strathfield.html

 

[So-smart]

Thanks soo much!