Write in the form a + bi:?

Question

-4 - sqrt(-32)/4

Answer 1

-4-sqrt(-32)/4
=-1-[isqrt(32)/4]
=-1-isqrt(2)

Answer 2

When you have a negative number being square rooted, you take out the square root to get the "i". So you will get when you solve:

-4 - √-32 /4

Then you get:

-4 - i√32 /4

Now take the square root of 32. Since it isn't a perfect square find a perfect square that can be multiplied with another number to get 32. That will be 16 x 2. So you will have:

(-4 - i√16 x √2) /4

Now you will have:

(-4 - 4i√2) /4

Now divide. Your answer will be:

-1-i√2 or -1-(√2)i

-1=a
√2=b

Answer 3

-4 - √(-32) / 4. [Factor out the largest square and -1 from the root.]
-4 - √[(16)(-1)(2)] / 4 [Simplify the square and the i.]
-4 - √(16)·√(-1)·√(2) / 4
-4 - 4i·√(2) / 4 [Simplify the fraction.]
-4 - i·√(2)

Note: If in your problem you forgot to write parentheses to include the -4 in the numerator, i.e. [-4 - √(-32)] / 4, simplify the root the same way, but when dividing by 4 at the end, you'd be left with -1 - i·√(2).

Answer 4

= -4 - sqrt(-32/16)
= -4 - sqrt(-2)
now...square of i = (-1)

so the eqn now becomes:
= -4 - sqrt((-1) x 2)
= -4 - i x sqrt(2)

Answer 5

(-4 - sqrt(-32))/4
(-4 - sqrt(-16 * 2))/4
(-4 - 4isqrt(2))/4
-1 - isqrt(2)
-1 - sqrt(2)i

Answer 6

-4 - sqrt(-32)/4
= -4 - sqrt(32)i /4
= -4 - i sqrt(2)