Complex Numbers-HELP PLEASE (1 Viewer)

chris_power_96 · Dec 17, 2012

The complex number z satisfies the equation arg(z+2)=pi/3
(i) Sketch the locus of the point P that represents z
(ii) Hence find the equation of the locus of P
(iii)Hence find the minimum value of |z-3|

I have completed i and ii, just don't have a clue on iii

Any help would be appreciated

HeroicPandas · Dec 17, 2012

part ii:
$y=\sqrt{3} (x+2)$
part iii:
$Importantly, you must know that the locus P is a straight line cutting the y-axis at 2\sqrt{3}$

$REMEMBER z - 3 starts at x = 3 and ends at z (in this case starts from x = 3, ends perpendicularly to y=\sqrt{3} (x+2)$

$\\Ultimately, the min distance is from x = 3 perpendicular to y=\sqrt{3} (x+2)$

^Its good to think about perpendicular distances when finding MIN distances

$and u must use perpendicular formula$

$\frac{|ax_1 +by_1 +c|}{\sqrt{a^2 +b^2}}$

$USING y=\sqrt{3}(x+2)$ $and the point (3,0)$

$REMEMBER TO PUT y=\sqrt{3}(x+2)$ $ INTO GENERAL FORM$

The answer is 5 units?
Whatever the answer is, it does not matter Chris_Power_96

Complex Numbers-HELP PLEASE (1 Viewer)

chris_power_96

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HeroicPandas

Heroic!

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