+163 In the complex plane, the graph of |z−3|=2|z+3| intersects the graph of |z|=k in exactly one point. Find all possible values of k.
Enter all possible values, separated by commas.
z is a complex number by the way.
+1094 Here is a hint:
Change z to a+bi. Since the magnitude is the square root of a^2+b^2, solve for that.
To make myself more clear, let me show you how to do the left side, and then you can to the right side.
Once we have changed z to a+bi, we can subtract 3 from a. This will give us (a-3)+bi.
Now, squaring a and b, we get
a^2-6a+9+b^2 for the inside of the square root. Therefore, the left side is √a2−6a+9+b2.
Now, try to do the right side, and solve the equation.
