Write 5 + sqrt(-75) as a complex number in simplest form.

Question

Q.  Write 5 + sqrt(-75) as a complex number in simplest form.

 

What would it be? Thank you ^-^ 

Answer 1

5 + √(-75)

 

 

Break up any radical terms by their factors.

 

5 + √(25)√(3)√(-1) =

 

5 + 5i√3

 

 

Factoring out a 5, we get

 

5(1 + i√3)

Answer 2

5 + √(-75) = 5 + √75 i

 

                = 5 + √25√3 i

 

                = 5 + 5√3 i