Question

Separate 3

√6 − √−12

into real and imaginary parts.​

Answer 1

Let `z=((3+sqrt(-1))/(2-sqrt(-1)))=((3+i)/(2-i))=((3+i)/(2-i))=((3+i))/((2-i))xx((2+i))/((2+i))`

`((3+i)(2+i))/((2-i)(2+i))=((6+i^(2))+5i)/((4-i^(2)))=(5+5i)/({4-(-1)})=(5(1+i))/(5)=(1+i)`.

`therefore" "|z|=sqrt(1^(2)+1^(2))=sqrt(2)`.

Hence, `z = (1 + i) and |z| = sqrt(2)`.