I am going to use ‘sqrt’ for the square root symbol.

Simplify:

sqrt(-32) – sqrt(-50) =

sqrt(16 x 2 x -1) – sqrt(25 x 2 x -1)

The sqrt(-1) = i, sqrt(16) = 4, and sqrt(25) = 5, so:

This equals 4i times sqrt(2) minus 5i times sqrt(2) by taking the square root of -1, 16, and 25.

This can also be written:

4isqrt(2) – 5isqrt(2)

Because they both have a base of sqrt(2), you can subract 5isqrt(2) from 4isqrt(2):

5isqrt(2) – 4isqrt(2) = -1isqrt(2)

= -isqrt(2)

To put it in a + bi form:

a – isqrt(2) = a + -isqrt(2)

This means a = 0, so

= 0 + -isqrt(2)

To make it 0+ bi:

The sqrt of 2 times -1 times i

= -sqrt(2)i or 0 + -sqrt(2)i

You can probably leave the 0 out because it doesn’t do anything (unless your teacher needs you to show it), so the answer is:

-sqrt(2)i

I hope this helps. If you need me to explain anything more or if you don’t understand something, let me know and I will try to help. 🙂