can someone please explain why imaginary number i squared is -1?????

Question

In my Algebra 2/ Trig.class we were trying to figure out why when i= -1 i squared also equals -1. Please help!!!

Answer 1

My teacher just told us that that is the way it is. I had a hard time with this too, we just learned it and have a test over it tomorrow. I wish I could help, but that's as much as I learned. Merry Christmas, don't forget that Jesus is the reason for the season!!!

PS In response to the previous answer,
~The square root of a negative number= i times that square root
~An imaginary number squared IS -1, we just can't figure out why. I wish I could help more, again I'm sorry ( :

Answer 2

explain imaginary number squared 1

Answer 3

the definition of i is i=√(-1), so i^2=-1
here is another way to think of i. When you multiply a number by -1 you go in a semi-circle on the number line where the center of the circle would be x=0 and the radius would be the absolute value of the number. multiplying by i, which is √(-1) you would go half-way, meaning you only do a quarter turn. this results in the fact that the line of multiples of i os found at right angles to the number line.
I hope this explanation helps.

Answer 4

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RE:
can someone please explain why imaginary number i squared is -1?????
In my Algebra 2/ Trig.class we were trying to figure out why when i= -1 i squared also equals -1. Please help!!!

Answer 5

If you multiply two radicals together and the number inside the radicals are the same, the result is the number inside the radical. Since i is DEFINED as the square root of negative 1, the operation of squaring i leads to -1

Answer 6

i = sqrt(-1), that is the definition of i.
Square both sides and get
i^2 = -1. QED

Answer 7

i does NOT equal -1. It is defined as the sqrt of -1.

Answer 8

i = sqrt(-1)
so
i^2 = i * i = sqrt(-1) * sqrt(-1)
= sqrt(-1)^2
= -1