38. what is (5+3i) simplified and the root of 9i times the root of 4i?

Question

math some one teach me how to classify my questions?

Answer 1

5+3i can not be further simplified.

root 9i times root 4i, roots cancel out and you are left with 9i*4i

9 times 4 is 36 i times i is i^2 which you learned equals -1 since i= sqrt of -1, i squared is simply -1, that means it is equal to -36

And I don't know what you mean by classifying the question..yeah...

Answer 2

Hi,
a) what is (5+3i) simplified?
This cannot be simplified.
If you intend "i" to be a real variable, then:
4i*9i =36i²
If you intend "i" to be imaginary, √(-1), then you can convert it into another form such as polar, but basically it cannot be simplified in rectangular form.

b) and the root of 9i times the root of 4i.
If "i" is imaginary, √(-1), then:
Then we have:
√(9i) *√(4i)
=√(9)*√(i)*√(4)*√(i)
=3*2√(i)*√i
=6[√(i)]²
=6i

If "i" is a real variable, then:
4i*9i =36i²

Another approach to solving this as an imaginary varible would be to take the square root of the imaginary number "i" which is .707....+.707...i. If you then squared that, once again you'd have "i." Note that you need to carry that out to the limit of the decimal places of your calculator or you'll get an incorrect answer.
So, it's much easier to do it the way I did it above.
Hope this helps.
FE

Answer 3

the foundation of 5+3i might properly be expressed as (a+bi), so (a+bi)^2=(5+3i) increasing the brackets and equating words, you get a^2-b^2=5, and 2ab=3, so a=3/2b, and (3/2b)^2-b^2=5, simplfying this does not extremely provide an easy type for b (and so no longer extremely a the two), yet it is the way you are able to pass approximately it.

Answer 4

squareroot of -4 or 2i and the second is 6i
38. first you have to get the i and 3 into like terms i is equal to the squareroot of -1, 3 is the square root of 9, 9 times -1 equals -9, -9 + 5 = -4 (still under the square root) You can simplify it further by getting out of the square root sign, split the -1 and the 4 (each under their own square root) the square root of 4 is 2 and the square root of -1 is i, 2 times i is 2i
Second question: again i = the squareroot of -1. that means i times i equals -1 (plain not squareroot) 4 times 9 = 36 and 36 times -1 = -36 since the entire problem is under the squareroot the 36 and -1 can split under their own squareroots and sqrt of 36 is 6, sqrt of -1 is i, i times 6 is 6i

Answer 5

5 +3i is already simplified ( i am assuming we are dealing with complex numbers)

(√(9i) )(√ (4i) ) = √ (36i^2) = 6i

Answer 6

(5+3i)
3i + 5 = 0
3i = - 5
i = -5/3

root of 9i = 3i
root of 4i = 2i
(3i)(2i) = 6i^2

Answer 7

first one is simplified and the second is -36