Re-express 3−32−−−−√
as a complex number with the imaginary unit i=−1−−−√
.(1 point)
To re-express 3−32−−−−√ as a complex number, we can multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 32−−−√ is 32+−−−√
So, we have:
3−32−−−−√ = (3−32−−−−√)(32+−−−√32+√)= (3⋅32)+(3⋅−−−√32)+(−32⋅−−−√)+(−32⋅−−−√)32+−−−√32+√= 96+−√−96+√32=((96+−√)−96)32+√=
Now, we can simplify further:
96+−√−96+√32=((96−96)+−√)32+√=(0+−√)32+√=−√2
what is all that garbage?
3-√-32 = 3 - 4√-2 = 3 - 4√2 i
that may not be what was meant, but the notation used is so unintelligible, that's just my best guess.
Apologies for the confusion in my previous response. You are correct, the correct re-expression of 3-√-32 is 3 - 4√2i. Thank you for providing the correct interpretation.
To re-express 3−32−−−−√ as a complex number with the imaginary unit i=−1−−−√, we can first evaluate the square root of -1, which is represented by the imaginary unit i.
The square root of -1 is represented as i. So, we have i = -1−−−√.
Now, let's express 3−32−−−−√ in terms of i.
We can rewrite the expression as:
3−32−−−−√ = 3−1/2
The numerator 3 can be written as 3*1.
So, we have:
3−32−−−−√ = 3*1−1/2
Now, we can substitute the value of i into the expression:
3−32−−−−√ = 3*1−1/2 = 3i−1/2
Hence, the re-expressed form of 3−32−−−−√ as a complex number with the imaginary unit i=−1−−−√ is 3i−1/2.