Question

Find all complex numbers which make the following equations true

|Z+1=1 and z² +1=1

Answer 1

Given:

 I z + 1 I = 1

 I z² + 1 I = 1

To Find

All the complex numbers make the following equations true

    I z + 1 I = 1 and I z² + 1 I = 1

Solution:

If  I z + 1 I = 1 holds true, then

                     z + 1 = 1.$e^{i2n\pi }$

                     z = 1.$e^{i2n\pi }$ - 1

                   z = 1.$e^{i2n\pi }$ - 1$e^{i2m\pi }$

If I z² + 1 I = 1 holds true, then

                  z² + 1 = 1.$e^{i2n\pi }$

                  z² = 1.$e^{i2p\pi }$ - 1

                  z²= 1.$e^{i2p\pi }$ - 1$e^{i2q\pi }$