How would √(-16) + √(49) be written as a complex number in the form of a + bi?

Question

How would
`√(-16) + √(49)` be written as a complex number in the form of a + bi?

Answer 1

`i=√(-1)\\\\√(ab)=√(a)\cdot√(b)\\\\√(a)=b\iff b^2=a\\--------------------\\\\√(-16)=√((16)(-1))=√(16)\cdot√(-1)=4\cdot i=4i\\\\√(49)=7\ because\ 7^2=49\\√(16)=4\ because\ 4^2=16\\--------------------\\\\√(-16)+√(49)=√(49)+√(-16)=\boxed{7+4i}`