complex numbers questions but focusing on part b
I know that its only sufficient for the case of equality but my working isnt foolproof
#Parts 4a/b
wise fossil
naive yarrowBOT
complex numbers questions but focusing on part b
I know that its only sufficient...
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fervent silo
Part b can be solved by visualising it in complex plane
|z| = distance of the point from origin
|z-2| = distance from 2 + 0i
Then use triangle inequality
For a
P(iy) = iy¹⁰⁶¹ - y¹⁰⁰² - iy +1
= iy(y¹⁰⁶⁰-1) - (y¹⁰⁰²-1)
Clearly y=1 is a solution.
Not sure if other solutions exits
timber wagon
👏
timber wagon
complex numbers questions but focusing on part b
I know that its only sufficient...
for part b) you can use definition of modulous so:\
$|x+yi|+|(x-2)+yi|\le 2$, $\sqrt{x^2+y^2}+\sqrt{(x-2)^2+y^2}\le 2$, $x^2+y^2\le 4-2\sqrt{(x-2)^2+y^2}+(x-2)^2+y^2$\ simplifying we get $0\le 4-2\sqrt{(x-2)^2+y^2}-4x+4$, so $4((x-2)^2+y^2)\le (8-4x)^2$ and $4x^4-8x+4+y^2\le 16x^2-64x+64$ and thus $y^2\le 12x^2+72x+60$ so $\boxed{-\sqrt{12(x^2+6x+5)}\le y\le\sqrt{12(x^2+6x+5)}}$
glad isleBOT
vengeance
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@wise fossil