solve y²=-16?

Answer 1

Actually, as we are getting into imaginary numbers anyways, we have to include both answers.

y² + 16 = 0 => (y + 4i)(y - 4i) = 0

so y = ±4i

As expected, there are two solutions, and they are conjugates of each other.

Answer 2

As you no doubt know, a square root is a number that when multiplied
by itself is equal to a given number. For example, 4 is the square
root of 16, since 4 x 4 = 16. Note, however, that -4 x -4 = 16, too.
We call 4 the positive square root of 16, and -4 the negative square
root of 16.

Now, you want to know if we can find the square root of a negative
number. Let's take -16. We need to find a number, call it x, such
that:
x times x (x^2) = -16

Now, we know that any number times itself must be positive, not
negative. Therefore, there is no such number x in the set of real
numbers.

A number x is defined, however, in the set of complex numbers. The
complex numbers are a superset of the real numbers. That is, the
complex numbers form a bigger set. The reals are a subset of the
complex.

A complex number has the form a + bi, where a and b are real numbers
and the i is a special number. The "a" is called the real part; the
"bi" is called the imaginary part. If we let a equal 0, then we have
an imaginary number. The set of imaginary numbers is also a subset of
the complex numbers. If we let b equal 0, then we have a regular real
number. This is why the reals are a subset of the complex: the reals
are just complex numbers that all have b=0, that is, no imaginary
part.

Now, the number i is defined to be equal to the square root of -1.
This means that i^2 (i squared) is equal to -1. So now we can find
the square root of -16.

Since -16 = (-1) 16, we can write:

sqr(-16) = sqr(-1) times sqr(16) (property of square roots)
sqr(-16) = i times 4

This is usually written as 4i. We can check by squaring 4i. We get
4 x 4 = 16 times i x i = sqr(-1) times sqr(-1) = -1, giving 16 times
-1 or -16.

There is much more to the complex and imaginary sets of numbers than I
can go into here. There are entire branches of mathematics (like
complex analysis) which deal with these numbers.

Answer 3

If that's the only information given, then:

y^2 = -16
y = (-16)^(1/2)
y = 4i

Answer 4

4i where i is the square root of -1

Answer 5

y^2=-16

y=SQRT(-16) = (-1)*16 = SQRT(-1)*SQRT(16) = 4i

Answer 6

can not be solved for y. impossible...
are you sure you wrote correctly?

Answer 7

either 4 or -4 i think neway

Answer 8

4i

Answer 9

4i

Answer 10

4i