00:01
So for this problem, we need to evaluate the following complex number.
00:04
For part a, we have the following operation that is the product between 5 plus 2 times j, which is a complex number, times minus 1 plus 4 times j, and this minus 5 times 5 times this expression right here.
00:36
So what we can do in here first is to try to solve this product in here between two complex numbers.
00:44
So by doing that product we obtain the following.
00:51
From there we obtain 5 times minus 1 that we know is minus 5.
00:57
We also have 5 times 4 so we will obtain 20 times j.
01:03
And this is now the other term is minus 2 times 1 which is minus 2 times j and the other one remember that the product between j and j should be equal to minus 1 so when we do this product right here we obtain minus 8 so simplifying this expression we will find that this is equal to minus 13 this is the real part and the imaginary part is equal to positive 18 times j.
01:45
So that's what we got from this product.
01:50
Now we need to sum this to this 5 times 6 degrees.
01:58
And we know that that 5 times 60 degrees corresponds to 5.
02:05
Times the cosine of 60 degrees plus j, which is the imaginary part, sign of 60 degrees.
02:17
So from this, we just need to simply substitute those values.
02:25
We will have that this is equal to minus, well, a positive value.
02:33
We have positive, so we have 2 .5 plus 4 .33 times 0 .3.
02:41
So we just need to subtract from this value, this value right here.
02:47
So then we will obtain that minus 13 plus 18 times j, minus 2 .5 minus 4 .33 times j.
02:59
So from this we obtain that the result from this is equal to minus 15 .5 in the real part.
03:10
And the imaginary part is 13 .67 times j.
03:16
So that's a solution for part a of this problem.
03:20
Now for part b, we are asked to calculate the following...