Question

If z = x + iy and | z + 6 | = | 2 z + 3| prove that x ^ 2 + y ^ 2 = 9

Answer 1

Answer:

Proved.

Step-by-step explanation:

|z|=|x+iy|=√(x^2+y^2)

Now, L.H.S.

|z+6|=|z|+|6|=√(x^2+y^2)+6

R.H.S.

|2z+3|=2|z|+|3|=2√(x^2+y^2)+3

From L.H.S. and R.H.S., we get;

√(x^2+y^2)=6-3=3

Therefore, x^2+y^2=9.