Det. z included in C(complex)...?

a. If Re z(it' s real part)=2 and z-i modulus is minimum





b.If img z = -1 and modulus of z-i-1 is minimum.





Thank you very much for any ideea!

Det. z included in C(complex)...?
a. the answer is z = 2 + i.


get the Argand diagram of the complex plane. Re z = 2 means the vertical line x = 2. The point closest to (0,1) is (2,1).








b. Im z = -1... this time we have a horizontal line y = -1.


The point closest to (1,1) is the point (1,-1)


Thus the answer is z = 1 - i.

















We can also do the analysis algebraically ... §


for question a.


you already know that z = 2 + bi.


z - i = 2 + (b-1)i


the modulus of that is 2^2 + (b-1)^2 ... the quadratic is minimum if b = 1.


Thus z = 2 + i.

radiata