Complex numbers locus Ty (1 Viewer)

[youngminii]

Find the minimum arg of z when the locus of z is |z - 3 + 4i| = 3
Thanks
The answer I'm getting is disagreeing to the one given.

 

[Timothy.Siu]

is it 16'16' degrees (nearest minute)

 

[cyl123]

Do you mean minimum magnitude wise or minimum based on number line (ie. more negative meaning smaller angle) ??

If its the first, then it would be -16'16'
Otherwise it would be -pi/2 (or -90 degrees) where z = -4i

 

[youngminii]

Do you mean minimum magnitude wise or minimum based on number line (ie. more negative meaning smaller angle) ??

If its the first, then it would be -16'16'
Otherwise it would be -pi/2 (or -90 degrees) where z = -4i

Well the teacher's answer was 0 (he was wrong in the working)
But yeah, apparently it's -pi/2.. Thanks

 

[tommykins]

-pi/2 once u draw the locus

 

[youngminii]

Hold up, how do you get 16'16'?
Let's change the question so it asks for max Arg
I keep getting -18'26'

 

[Timothy.Siu]

90-2sin^-1 3/5

 

[youngminii]

90-2sin^-1 3/5

Sorry to keep on bugging you, but how did you get this?
Is it possible to post up full solution?

 

[Timothy.Siu]

Sorry to keep on bugging you, but how did you get this?
Is it possible to post up full solution?

well, once u draw it, u can work out the distance from the origin to centre as 5units and u know the radius is 3, and that the tangent makes a right angle to the centre of the circle so u can use basic trig to work out the angles

 

[youngminii]

well, once u draw it, u can work out the distance from the origin to centre as 5units and u know the radius is 3, and that the tangent makes a right angle to the centre of the circle so u can use basic trig to work out the angles

Got it, thanks
I wonder why my previous method didn't work :S

 

[tommykins]

max arg = atan (-1/3)

 

[cyl123]

no that gives angle of around -18, which is not the maximum since line from origin to circle forming that point is not a tangent to circle. max and min args are found by taking arg of tangents

timothy is right... angle is found by taking tangent to the circle.

 

[hungwell1337]

what a beast