Question

write √-4+10 in a+bi form

Answer 1

Do you understand how the square root of a negative number works?

Answer 2

- Nope .

Answer 3

The square root of negative 1 is defined as the imaginary number "i". I'm sure that sounds weird at first, but don't worry :)

\[\sqrt{-1} = i\]
And...
\[(\sqrt{-1})^{2} = i^{2}\]
which means that...\[(\sqrt{-1})^{2} = -1 = i^{2}\]

Answer 4

So, any time you have a square root with a negative number under it, just imagine it as the positive number multiplied by a negative 1. For example:\[\sqrt{-25} = \sqrt{(25)*(-1)}\]
And then you can take the square roots of each part...
\[\sqrt{-25} = \sqrt{(25)*(-1)} = \sqrt{25}*\sqrt{-1} = 5 * i\]

Answer 5

- oh okay , i get that .

Answer 6

Good :)

So, your question is:
Write √-4+10 in a+bi form

So, using what we just talked about, what is the square root of -4?

Answer 7

2

Answer 8

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

Answer 9

- Okay .

Answer 10

Square root of -4 is square root of 4 multiplied by square root of negative 1.

The square root of 4 is 2 (you got that part right!) and square root of negative 1 is "i".

So:\[\sqrt{-4} = \sqrt{(4)(-1)}=\sqrt{4}\sqrt{-1} = 2i\]

Answer 11

- Okay .

Answer 12

To write √-4 + 10 in "a + bi" form,
you just write the real number part (10, in this problem) as the "a"
and the imaginary part (2i in this problem) as the "bi" part.

so:
√-4 + 10 = 10 + 2i

Answer 13

(:

Answer 14

- iget it .

Answer 15

Great :) Glad to help...