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Further maths help needed!!!

Given that z is a complex number, such that Iz-iI=1, find the greatest and least values of Iz+1I.

Can someone give me some insight on where to start with this question?

Reply 1

ghostwalker

Original post by Juliakinga

Given that z is a complex number, such that Iz-iI=1, find the greatest and least values of Iz+1I.

Can someone give me some insight on where to start with this question?

A geometric approach would be easiest.

Draw the locus of points satisfying |z-i|=1. Then what's z+1? And hence ....

Reply 2

Juliakinga

Original post by ghostwalker

A geometric approach would be easiest.

Draw the locus of points satisfying |z-i|=1. Then what's z+1? And hence ....

So Iz-iI=1 is a circle, would Iz+1I be the point -1

Reply 3

Juliakinga

Original post by ghostwalker

A geometric approach would be easiest.

Draw the locus of points satisfying |z-i|=1. Then what's z+1? And hence ....

So Iz-iI=1 is a circle, would Iz+1I be the point -1

Reply 4

RDKGames

Study Forum Helper

Original post by Juliakinga

So Iz-iI=1 is a circle, would Iz+1I be the point -1

The first one is a circle is a circle of radius 1 around the point (0,1).

|z+1| is the distance between the point (-1,0) and any point z on that circle.

Can you see what the minimum and greatest possible distances are? A sketch is important here

Reply 5

username4167452

Original post by Juliakinga

Given that z is a complex number, such that Iz-iI=1, find the greatest and least values of Iz+1I.

Can someone give me some insight on where to start with this question?

draw a sketch. its asking for the shortest and greatest distance between (-1,0) and the circle. so draw a line from (-1,0) to the furthrest point on circle and line from (-1,0) to the closest point on the circle from (-1,0). Try and notice a way to calculate these distances, given you know the radius and distance formula

Reply 6

ghostwalker

Original post by Juliakinga

So Iz-iI=1 is a circle, would Iz+1I be the point -1

No, it's not a point; |z+1| is a function returning the modulus of z+1, (given that z is on the original circle.)

RDKGames and Physikoi have given you one method.

I was doing it in smaller steps, which is why I was asking what is z+1, given z lies on our circle, and hence |z+1|.