Question

Please help me in this maths question. Thanks

Answer 1

Answer:

the answer is in the above attachment

Answer 2

We see that the line containing the origin and the point of least argument p in B forms a tangent to the circle |z−u|=1. The segment of this line between the two points has length 22–√ and is the hypotenuse of a right triangle with one leg of length 1 (corresponding to the circle's radius). Therefore the length of the other leg, which is also the modulus of p and the answer to the question, is

(22–√)2−12−−−−−−−−−−√=7

With notation of z=x+iy

You have to solve the equation of

|z-(2-2i)|^2\leq 4 for Re(z)=x

(Re(z)-2)^2+(Im(z)+2)^2\leq 4

From this

Re(z)\leq\sqrt{4-(Im(z))^2}+2

For maximum Im(z)=y=0

So you will get the maximum value of Re(z)

You can read down it from your sketch, too