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# FP1 complex numbers/loci help watch

1. I am stuck on the question:

Find the greatest and least value of arg z if | z + 2i | = 1.

I have gathered that the locus is a circle with centre -2i with a radius of 1, and that the min/max arguments occur on points of tangency with the circle, however I do not know how to work out exactly what these angles are.

Please help? If you work it out please give a step to step guide on how you calculated it so that I can understand.

Thanks.
2. (Original post by ♥Samantha♥)
I am stuck on the question:

Find the greatest and least value of arg z if | z + 2i | = 1.

I have gathered that the locus is a circle with centre -2i with a radius of 1, and that the min/max arguments occur on points of tangency with the circle, however I do not know how to work out exactly what these angles are.

Please help? If you work it out please give a step to step guide on how you calculated it so that I can understand.

Thanks.
draw a good diagram
look for right angled triangles
3. (Original post by ♥Samantha♥)
I am stuck on the question:

Find the greatest and least value of arg z if | z + 2i | = 1.

I have gathered that the locus is a circle with centre -2i with a radius of 1, and that the min/max arguments occur on points of tangency with the circle, however I do not know how to work out exactly what these angles are.

Please help? If you work it out please give a step to step guide on how you calculated it so that I can understand.

Thanks.
Z is a line from the origin to the centre of the circle to the edge of the circle. The min is the smallest distance to the circle. Max is furthest.
4. (Original post by BinaryJava)
Z is a line from the origin to the centre of the circle to the edge of the circle. The min is the smallest distance to the circle. Max is furthest.
It would have been if the min/max modulus was required ...
5. (Original post by TeeEm)
draw a good diagram
look for right angled triangles
Lol I feel so stupid now.... I just drew it and it's really simple I feel quite silly for spending almost an hour this morning on this.

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6. (Original post by ♥Samantha♥)
Lol I feel so stupid now.... I just drew it and it's really simple I feel quite silly for spending almost an hour this morning on this.

Posted from TSR Mobile
it happens... all the best

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