Question

How do I simplify the expression 4+√-4+i
i being an imaginary number.

Answer 1

Is that

\[4 + \sqrt{-4} + i\]

or

\[4 + \sqrt{-4 + i}\]

Answer 2

The first one

Answer 3

Oh ok, thank you.

Would you agree that

\[\sqrt{-4} = \sqrt{(-1)(4)} = \sqrt{-1} * \sqrt{4}\]

Answer 4

Yes

Answer 5

And \[\sqrt{-1} = i\]

Answer 6

Yes, isnt also i^2 -1

Answer 7

That is true as well

Answer 8

So we see how

\[\sqrt{-4} = \sqrt{-1} * \sqrt{4} = i * 2 = 2i\]

Answer 9

Ohh I see

Answer 10

So would my answer be 4+3i ?

Answer 11

Yes, that is right

Answer 12

Oh Ok, Thank you!