00:01
I have given here the function in terms of three complex numbers, z1, z2, and z3, f, signum, for this function here, and determinant.
00:15
Where we have signal max as defined as x over, mod of x is x not equal to 0, and we have signum 0 is equal to 0.
00:24
Now for a not equal to 0, we'll check the relation here.
00:29
So in the options we are given here, we'll to find out first f, az1, az2, az2, az2, let's just write the function here again in terms of x over here, modulus x.
00:42
So that can be given as we get f equals there'll be x.
00:57
So 1 -1 -1, z1, z2, z3, z1 conjugate, z2 conjugate, that 2 conjugate, that's the second here.
01:12
Now this symbol here stands for determinant here, it is all divided by mod, so divide by we have the mode of x.
01:23
Maybe a determinant that is coming out to be one one one then z one that one that two that three then z one conjugate that to conjugate that three conjugate so we're to find out now as a z one a two a that three so for that function becomes and that it as one one one a z one then a z two then a z two then then a z3, then a z1 conjugate, a z2 conjugate, a z3 conjugate, or divide by, we have n modulus, then determinant, so we have a z1, a z2, a z3, then we have a z1 conjugate, a z2, a z3, then we have a z1 conjugate, a z2 conjugate, a z3 conjugate.
02:52
Now, if we have a is a real value, or even let us say here, let a be a complex number.
03:02
So what we can do, let it be a complex number.
03:05
So this part here, we have, we'll just look at here this term.
03:11
We have all conjugate, az1, will be given as a conjugate, then z1 conjugate.
03:17
And similar for this.
03:19
What you can observe here in a second row in this determinant here we have, it is a, a, a, we can factor out that so it's coming out to be here a and we can erase this next from third row will be a conjugate z1 conjugate in this property a conjugate that to conjugate a conjugate a conjugate that three conjugate so from here we'll factor out a conjugate we just remove this similarly here we have in denominator we can factor out a and a conjugate...