Algebra II, imaginary unit problems...?

Question

For some reason they confuse me, if someone could help me...

√-405
√-175

is -2i a solution of x² = -4
is -2√2 a solution of x² = -8

4x²+20=0
x²-8x+20=0

I don't understand how to convert the i to a regular number.

Answer 1

√-405 = √(405) i = 9√(5) i
√-175 = √(175) i = 5√(7) i

√-1 = i
-1 = i^2
-√-1 = i^3
1 = i^4

x²-8x+20=0
x = 4±√(16-20) = 4±2i, used the quadratic formula.

Answer 2

'i', or 1i, the unit on the imaginary number line is called imaginary because it is not part of the real number set.

The solution to the square-root of negative numbers is not a real number, but it still exists in the imaginary dimension.

Same thing for parabolas (the bottom 2 equations),. When you draw a parabola where the vertex is at or below the origin (x=0, y=0), the parabola crosses the x-axis at 2 places (or one place if it is right *on* the origin). The solutions, or zero's to the equation are real numbers: x is some real value (or 2 real values).

Now draw a parabola *above* the x-axis. Where are the zeros? The parabola does not cross the x-axis, so there are no *real* solutions -- only *imaginary* solutions.

Imaginary numbers (and complex numbers -- 2-dimensional numbers with real and imaginary components) are used in solving higher mathematical equations, called differential equations. They are used in electrical engineering and other engineering work to solve complex problems everyday.

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Answer 3

Yes, -2i is a solution of x² = -4
Yes, -2√2 is a solution of x² = -8

i is an imaginary number meaning the square root of -1, it cannot be converted to a 'regular' number.

4x^2 + 20 = 0
4x^2 = -20
x^2 = -5
x = +/- sqrt(-5)
x = +/-sqrt(5)*i

Answer 4

-2sqrt2 is NOT a solution of x^2=-8 as no sqare of a real number is negativ
-2i is a solution of x^2=-4

Answer 5

the only way to make i into a regular number is to square it.

i^2 = -1

That is the only way it can be a regular number...... the rest of the time it is just an imaginary number.

Answer 6

The answer to both of your questions is yes.