My teacher told me that square root of negative 1/4 = plus/minus half i. Is this correct?

Question

My teacher told me that square root of negative 1/4 = plus/minus half i. Is this correct? I thought that only when s^2=5 then s=+/- square root 5 but when or nvm.

Please explain and any examples would be appreciated.

Answer 1

teacher knows best

Answer 2

1/2 x 1/2 = 1/4 so +/-1/2 is the square root of 1/4. Since it is negative and the square of -1 = i the answer is +/-1/2 i.

Answer 3

I believe the focus of your question is on the +/- 2. This simply means that both +2 and -2 when squared, give you +4. And of course, the imaginary 'i' is there because you cannot take the square root of a negative number. If you were to plot the equation y = x^2 on graphic paper, you would get a parabola and 2 of the points on the parabola would be (2, 4) and (-2, 4). Any equation of the second degree (i.e. the highest exponent is 2) produces a parabola which confirms that for each value of y, there are 2 values of x; Except for the maximum or minimum point which is usually found by taking the derivative of the equation.

Answer 4

? What is nvm?
Your teacher is right on, almost!
Look at it this way:
The positive square root of 1/4 is 1/2. The
negative square root of 1/4 is -1/2.
If we want the 2 square roots of -1/4 we
must multiply the 2 values above by √-1 or i.
So the 2 square roots of -1/4 are 1/2*i
and -1/2*i.

Answer 5

Your teacher is correct.

In your second sentence, you also are correct... up to "...but ". After that I don't know what you're saying.

Square roots (or even roots) of negative numbers numbers don't exist within the real no. system. Including the imaginary (or non-real) number system provides answers. (The two taken together -- real and non-real --
make the complex number system.)

i = one of the sqrt of (-1)
plus or minus i^2 = -1
i^3 = -i
i^4 = 1

Thus any power of i simplifies to one of these 4 forms; and the real numbers have been expanded by the imaginary to become the complex, where all numbers are considered to be of the form: a + bi, where a and b are real number coefficients.

Answer 6

That is correct because i stands for imaginary numbers. In math you are not supposed to take the square root of a negative number. Thats why you add i. i= square root of -1, i squared = -1, i to the fourth= 1.

Answer 7

That´s right because:
(-1/2) x (-1/2) = +1/4 = 1/4
or
(+1/2) x (+1/2) = +1/4 = 1/4

A positive number as element of R has two roots: one is negative and another is positive.
Kisses!

Answer 8

Yes.

If you multiply (1/2)i by itself, and use iXi = -1, you get 1/4. Check the other answer the same way.

Here is another example: x^2 = -9

x = 3i or x = -3i.

Here is another, related, example:

X^2 = + 9

x = 3 or -3.

Answer 9

Yup - it's good to know she got it right.

1/2 times 1/2 is a quarter, so the sq rt will contain1/2 (+ or -)

A negative number must have i in its sq rt.

1/2i times 1/2i = -1/4

or -1/2i times -1/2i = -1/4

Good luck and well done for being so industrious over Xmas

Answer 10

Yes. That is correct. Because Sqr(-1/4) =sqr(1/2i)^2=+-1/2i Ans.