Question

if z= -2-2i/i find |z|
please solve this answer.
​

Answer 1

Answer:

Let z=x+iy. Then, ∣z∣=  

x  

2

+y  

2

 

​

 and z+1+2i=(x+1)+i(y+2).

∴∣z∣=z+1+2i

⇒  

x  

2

+y  

2

 

​

=(x+1)+i(y+2)

⇒  

x  

2

+y  

2

 

​

=x+1 and y+2=0

⇒x  

2

+y  

2

=(x+1)  

2

 and y=−2

⇒x  

2

+4=(x+1)  

2

 and y=−2

⇒x=  

2

3

​

 and y=−2

Hence, z=x+iy=  

2

3

​

−2i