All the powers are added they dont make 10

[morbello]

i would like to know why or how the following comes about.

when j^10 =(j^4)^2j^2=1^2(-1)=1

why from ^10 does a J^4 squared and a j^2 when all the powers are added they don't make 10.

could you tell me a little about it.

 

[CompuChip]

why from ^10 does a J^4 squared and a j^2 when all the powers are added they don't make 10.

Oh, but they do. Remember that (j^4)^2 = (j^4) (j^4).

On the other hand, 1^2 x (-1) is not 1

 

[morbello]

Oh, but they do. Remember that (j^4)^2 = (j^4) (j^4).

On the other hand, 1^2 x (-1) is not 1

so it is about making the powers add up,this is good I am a second year science student but i could not remember the maths on this one ,im working though a book to get to know this kinda stuff.thank you for your help.

 

[CompuChip]

Actually you should remember these rules:

• aⁿ * a^m = a^{m + n}
• (aⁿ)^m = a^m*n

(for a real) for the rest of your life. If you forget them, you can go back to the case where n and m are integer numbers and write it out, for example:
$$a^3 \times a^4 = (a \times a \times a) \times (a \times a \times a \times a) = (a \times a \times a \times a \times a \times a \times a) = a^7$$
whereas
$$(a^3)^4 = (a \times a \times a)^4 = (a \times a \times a) \times (a \times a \times a \times a) \times a \times a \times a) \times (a \times a \times a \times a) = (a \times a \times a \times a \times a \times a \times a \times a \times a \times a \times a \times a \times a \times a) = a^{12}$$

 

[morbello]

hello again I've another one for you.

on the equation (4-j3)^2 =16-j24-9

i can see were the 16 and the 9 comes from but were does the j24

 

[noumed]

hello again I've another one for you.

on the equation (4-j3)^2 =16-j24-9

i can see were the 16 and the 9 comes from but were does the j24

multiply it out,

(4 - j3) (4 - j3)

you'll see that there'll be a -j24 from the multiplication of the real number and the complex number.

 

[morbello]

well i did 4*4+-3*4+-3*-3+3*-3 but i got 25

is there some thing wrong with my results.is the -j24 as were the j is a number=-1

 

[noumed]

j is a representation of the square root of -1, think of it as a variable.
i don't think you did the multiplication right.

(a - b)^2 = (a - b) (a - b) = a^2 - 2ab + b^2

 

[morbello]

no but i think I am getting used to it thank you for your help.