00:01
So in the given question we are told that if the modulus of z plus 9x.
00:08
Is equal to 6 we are told to find the greatest value that z the modulus of z can have.
00:18
The greatest value of modulus of z, right? so we can start from modulus of z and write it as modulus of z plus.
00:30
9 by z minus 9 by z right so this is same as writing modulus of z since these two terms cancels off so now what we are going to do is to use a property of complex numbers by which we can write if z1 plus z2 the modulus of z1 plus z2 is taken it will be less than or equal to the modulus of z1 plus the modulus of z2.
01:02
So we are going to use this property over here.
01:06
So what we are going to do is to take modulus of z would be then less than or equal to this is taken as z1 and this is taken as z2.
01:20
So we will have modulus of z plus 9 by z plus modulus of minus 9 by z right so this is what we would have and now let's take the modulus over here so modulus of z is less than or equal to the value of this is already given in the question as 6 so 6 plus modulus of minus 9 by z now the next property that we are going to use is that when we take the modulus of z 1 by z 2 we can take it as modulus of z1 divided by modulus of z2.
02:02
So let's use this property for taking the modulus of minus 9 by z then we will have 6 plus modulus of minus 9 divided by modulus of z and this would be equal to this would be equal to 6 plus 9 by modulus of z...