Question

Complex numbers help. *question attached below*

Answer 1

So I have already found the first part of this question, which is 1+2i but I am stuck at the second part. I know the diagram needs to show a circle centered at (1,2i), with a radius of √5, but how do I find the greatest value of |z| subject to this condition?

Answer 2

isnt |z| the distance from the origin?

Answer 3

if so, then consider a point in the circle centered at 1,2 of radius sqrt5, and distance it from the origin

Answer 4

Isn't z the distance from z1?

Answer 5

(x-1)^2 + (y-2)^2 = 5

x=x, y=sqrt(5-(x-1)^2)



i think z is some complex number and |z| is its 'distance' from the origin

Answer 6

|z| = sqr(zz*) might be a better definition, but i have no texts other than wolfram to verify it

Answer 7

so z is said to be the set of complex numbers that create the circle ...

|z| is the modulus of any of the complex numbers on the circle

Answer 8

given z=a+bi

|z| = sqrt(a^2+b^2) which of course is just the distance a point is from the origin

Answer 9

so, when

d^2 = x^2 + 5-(x-1)^2

is at its max