Hello Guys Hope you are Fine
How to determine the Numbers complexes Z such as:
Z, Z (2), 1+Z has the same Module?
Thanks in Advance Guys
So, we have to find such as .
The first equality can be written as or .
If , but must be 0.
If and , we have to solve the system:
or
Substracting the first equation from the second we get .
Now, plug in the first equation and solve for .
We get or .
So, there are two complex numbers satisfying the problem:
and