Need Help: Simplifying Expressions

[Necto]

The question says: Simplify each of the following expressions:

. . .\(\displaystyle -j^{29}\, +\, 2j^{32}\, -\, j^{5}\)

I also have the answer to this question, but I just need some explanation on how to solve this expression step by step.

. . .\(\displaystyle =\, -j(j^{28})\, +\, 2j^{32}\, -\, j(j^4)\)

. . .\(\displaystyle =\,-j(1)\, +\, 2(1)\, -\, j(1)\)

. . .\(\displaystyle =\,2\, -\, 2j\)

Thank you in advance, I greatly appreciate it.

 

[Deleted member 4993]

The question says: Simplify each of the following expressions:

. . .\(\displaystyle -j^{29}\, +\, 2j^{32}\, -\, j^{5}\)

I also have the answer to this question, but I just need some explanation on how to solve this expression step by step.

. . .\(\displaystyle =\, -j(j^{28})\, +\, 2j^{32}\, -\, j(j^4)\)

. . .\(\displaystyle =\,-j(1)\, +\, 2(1)\, -\, j(1)\)

. . .\(\displaystyle =\,2\, -\, 2j\)

Thank you in advance, I greatly appreciate it.

You have been given step-by-step solution.

The thing you need to know is:

j = √(-1) → j⁴ = 1 → j^4*n = 1 → j⁴ = j^4*7 = j^4*8 = 1

Now tell us, where the problem is - exactly.

 

[ClaireWu]

The question says: Simplify each of the following expressions:

. . .\(\displaystyle -j^{29}\, +\, 2j^{32}\, -\, j^{5}\)

I also have the answer to this question, but I just need some explanation on how to solve this expression step by step.

. . .\(\displaystyle =\, -j(j^{28})\, +\, 2j^{32}\, -\, j(j^4)\)

. . .\(\displaystyle =\,-j(1)\, +\, 2(1)\, -\, j(1)\)

. . .\(\displaystyle =\,2\, -\, 2j\)

Thank you in advance, I greatly appreciate it.

we can use the formula j^(2n) = (-1)^n for all positive integers of n too