# Math Assistance

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#### shermaine

##### New Member
For Q2.jpg: How to i get the equation on the right side from the left?

For Q3.jpg: If i want replace all s with jw. Can i said s^4 and s^2 will have positive sign (+) and s^3 and s will have negative sign (-)?

For Q4: How to i get the matrix?

Thanks!!

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#### MrAl

##### Well-Known Member
Hi,

Q2: The equation on the right is the numerator of the equation on the left.

Q3: j is the sqrt(-1), so j^2 is considered to be -1, and (-1)^2 is the same as j^4 so that equals 1.

Table:
j^1= j
j^2= -1
j^3= -j
j^4= 1

and for powers over 4 repeat the same pattern:
j^5=j^1= j
j^6=j^2=-1
j^7=j^3=-j
j^8=j^4=1

etc.

and note all we did was subtract 4 from the exponent repeatedly until the exponent is 4 or less. So:

j^9=j^(9-4)=j^5=j^(5-4)=j^1=j

and also for example j^15:
j^15=j^(15-4)=j^(11)=j^(11-4)=j^(7)=j^(7-4)=j^(3)=-j

Q4:
Take the transpose of the matrix and multiply by the matrix in that exact order, then calculate the inverse matrix.

Last edited:

#### shermaine

##### New Member
Hi MrAl,

But for Q2, i still not able to get it. I try to multiply the equation on the left with all numerator and denominator with sTi (S + 1) and solve it, but my question doesnt get the equation on the right.