# Math

posted by .

i^6 = (i^2)^3 = (-1)^3 = -1

The square, not the square root of -1 is 1. :)

B.t.w., can you prove that -1 times -1 is 1? Hint, try to prove first that for any number X:

-1 times X equals -X

How do you find the square root of -1?

The square of any real number is alwayspositive. This means that if you want to define the square root of minus 1 you have to extend the real number system. Mathematicians have invented imaginary and complex numbers to deal with this.

The square root of minus one is denoted by i. So, by definition:

i^2 = -1

Complex numbers are numbers of the form a + bi, where a and b are real numbers.

So, e.g.

(1 + i)^2 = 1 + 2 i + i^2 = 2 i

Actually, we can't take the square root of a negative number. Mathematicians have a way. To find the square root of a negative number, take the square root, as if it were a positive number, then add the letter "i" (the i stands for imaginary). Therefore, the square root of -1 is 1i.

Suppose / is equal to square root symbol and ^ is the power

Then what would this be

/-1^6

It is 1.You see when you take a negative number and multiply it to a negative number it becomes a positive.
example:
-1*-1=1
when you take a positive number and multiply it to a negative number then it stays negative:
example:1*-1=-1

• Pre-Algrebra -

it's about distributive property

simplify the expression

12xy-4xy

• Math -

8xy

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Math

What is the square root of 12? 3.464 Well, that's true, but you could simplify it in radicals. The square root of 12 is the same as saying the square root of 3 times the square root of 4. The square root of 4 is plus or minus 2, so
2. ### Math Help

the square root of 3 times the square root of 15 also the square root of 18 times the square root of 3 To multiply square roots: sq rt of z times the sq rt of y It would be the square root of zy The first one is 3x15 = 45 So it's the …
3. ### Math

Just need some help... Directions: Multiply or raise to the power as indicated... Then simplify the result. Assume all variables represent positive numbers. 1. 5(square root of 6) times two-thirds(square root of 15)= 3 one-third (square …
4. ### Algebra

Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities. I don’t understand how to compute these. Also I don’t have the square root sign so I typed …
5. ### math

Nakim simplified 3 times the square root of 2x plus x times the square root of 8x minus 5 times the square root of 18x and got -10x times the square root of 2x for an answer. Part 1: Using complete sentences, explain what Nakim did …
6. ### Math simplifying mixed radicals

Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed …
7. ### Math ~CHECK MY ANSWER~

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers?
8. ### Math ~CHECK MY ANSWERS~

1) Which of these is a rational number? a. Pi b. square root 3 ****** c. square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers?
9. ### Calculus

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum?
10. ### math

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers?

More Similar Questions