Finding complex z, z-1, z^-1 with same modulus

[oiler90]

My nephew asked me for help with this problem but I'm stumped so far.

 

[Ishuda]

My nephew asked me for help with this problem but I'm stumped so far.

Where are you stuck?

If z is a complex number, it can be written as
z = a + i b
where i is the square root of minus one and z-1 can be written as
z-1 = a-1 + i b
Find the modulus of these two numbers and set them equal to each other. That will give you a value for a.

Now find the modulus of 1/z and set it equal to the modulus of z. Since you know the value of a, this will give you the value of b (actually two values).