i don't understand why (j)(j)(-j) when converted to polar form is 1∠90°. How do one get 1∠90°?

 

i don't understand why (j)(j)(-j) when converted to polar form is 1∠90°. How do one get 1∠90°?

multiplication is associative so we can write (j)(j)(-j) as ((j)(j))(-j)
(j)(j) = -1 and (-1)(-j) = j
|j| = 1 and ∠j = 90°

Pretty simple and straight forward.

 

Think of j as a rotation operator that rotates a vector on to the y-axis or j-axis.
Thus (1 + j) is a counter-clockwise rotation 45°.
(0 + j) is a counter-clockwise rotation 90°.
(0 - j) is a clockwise rotation 90°.

Hence (j)(-j) would cancel each other.

(j)(j)(-j) = (j) = (0 + j) = 1∠90°

https://en.wikipedia.org/wiki/Complex_plane

 

i don't understand why (j)(j)(-j) when converted to polar form is 1∠90°. How do one get 1∠90°?

Remember the definition of j. It is the value that, when squared (multiplied by itself) yields -1.

So (j)(j) = -1 leaving you with (-1)(-j).

Then -x is the same as (-1)(x), so (-j) = (-1)(j), so now you have

(-1)(-j) = (-1)(-1)(j)

Then you know that (-1)(-1) = 1 leaving you with just j.

The only thing left is to realize that j = 1∠90°.

Do you understand why this is the case? If not, we can go into that.

 

i don't understand why (j)(j)(-j) when converted to polar form is 1∠90°. How do one get 1∠90°?

Hi,

In addition to the other good suggestions here, it would help for you to look up the complex plane and see how that works.

 

Thank you all, it all makes sense now,