HELP: Complex Numbers Locus Question (1 Viewer)

WhoStanLeee · Dec 20, 2014

Hey,

I can't seem to find the Locus for Question 22. a) I have completed the proofs above, but can't seem to find the locus of w, when lzl = 2.

Thanks for the help!

FrankXie · Dec 20, 2014

WhoStanLeee said:
Hey,

I can't seem to find the Locus for Question 22. a) I have completed the proofs above, but can't seem to find the locus of w, when lzl = 2.

Thanks for the help!

$when $ |z|=2, x^2+y^2=|z|^2=4, $ sub. this into $ u $ and $ v, u=x-\frac{x}{4}=\frac{3}{4}x, v=y+\frac{y}{4}=\frac{5}{4}y. $ Now from these solve for $ x $ and $ y, x=\frac43u, y=\frac45v. $ therefore, $ \left(\frac43u\right)^2+\left(\frac45v\right)^2=4, $ so the locus is$

$\frac{u^2}{\left(\frac{3}{2}\right)^2}+\frac{v^2}{\left(\frac{5}{2}\right)^2}=1$

WhoStanLeee · Dec 20, 2014

The solutions have

100x^2 + 36y^2 = 225

FrankXie · Dec 20, 2014

yes exactly the same, i wrote that way is to easily see what are semi-major and semi-minor axes of the ellipse.

HELP: Complex Numbers Locus Question (1 Viewer)

WhoStanLeee

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FrankXie

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WhoStanLeee

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FrankXie

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