Help with complex number (1 Viewer)

[HeyJes]

1) sketch the locus of z if |z-3+3i| <= 2
2) find the maximum value of |z|

Help with the second part only please?

 

[h_im3lda]

well, the max value of |z| is the distance from origin through the centre of the circle which is (3,-3) and all the way to the edge of the circle
so |z|=distance to the centre of the circle+ radius = √(9+9) + 2 = 3√2+2
Drawing it will always help.
Hope this helps

 

[asianese]

Have a look. I accidentally cut it off: I meant

 

[HeyJes]

View attachment 25926

Have a look. I accidentally cut it off: I meant

I know that but why is this the furthest point? (I just feel like it is , but I can't prove it)

 

[Carrotsticks]

I know that but why is this the furthest point? (I just feel like it is , but I can't prove it)

To really confirm it, you can use the Reverse Triangle Inequality. Similarly, you could find the minimum |z| using the normal Triangle Inequality.

 

[HeyJes]

To really confirm it, you can use the Reverse Triangle Inequality. Similarly, you could find the minimum |z| using the normal Triangle Inequality.

You could split it like that?
Generally how to split |z-a|?

 

[Carrotsticks]

You could split it like that?
Generally how to split |z-a|?

Well you need to justify and state that you're using the Reverse Triangle Inequality. In general: