Solve this problem

Question

Answer 1

√-16 = (√16)(√-1) = 4i

(√-3)(√-3) = -3

√(-4)(√-4) = -4

3i² = 3(√-1)(√-1) = 3(-1) = -3

3i³ = 3(-1)i = -3i

Putting it all together:

4i - (-3) - (-4) + 3i - (-3) + (- 3i)

4i + 3 + 4 + 3i + 3 - 3i

10 + 4i

Answer 2

First you need to get rid of all the square roots of negative numbers as follows

√(-16) = 4i

√(-3) = i√(3)

√(-4) = 2i

You will get

4i - (i√(3))² - (2i)² + 3i - 3i² + 3i³ = 4i - 3i² - 4i² + 3i - 3i² + 3i³

Then combine like terms

7i - 10i² + 3i³

Finally, substitute i² = -1 and i³ = -i, and combine like terms again

7i - 10i² + 3i³ = 7i - 10(-1) + 3(-i) = 10 + 4i