#The sum of the square of the modulus of the elements in the set
mild topaz
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plucky sleet
Hmmm
long hawk
First of all, what do these sets look like?
mild topaz
First of all, what do these sets look like?
its set of complex numbers which follows these two conditons z-1 lessthan equal to 1 an and z-5 less than equal to z-5i
long hawk
its set of complex numbers which follows these two conditons z-1 lessthan equal ...
Well, yeah... But what do they look like on the complex plane?
Hint: take z = x + iy, then the inequalities are transformed to real-number inequalities.
mild topaz
not able to think more than this
long hawk
Note that if a > 0, then |f(x)| > a is equivalent to f(x)^2 > a^2, and the same for any other of the three signs.
Thus, the first inequality |x - 1 + iy| ≤ 1 is equivalent to (x - 1)^2 + y^2 ≤ 1.
mild topaz
Thus, the first inequality \|x - 1 + iy\| ≤ 1 is equivalent to (x - 1)^2 + y^2 ≤...
should not it be this?
long hawk
should not it be this?
z^2 and |z|^2 are not the same thing for complex z.
If z = x + iy, then |z|^2 = x^2 + y^2.
long hawk
Alright, and now try the same thing for the second inequality.
long hawk
yeah then ur statement is rightt
I recommend drawing the coordinate axes, by the way.
long hawk
No need for cases. |x - 5 + iy| ≤ |x + (y - 5)i| is equivalent to (x - 5)^2 + y^2 ≤ x^2 + (y - 5)^2.
mild topaz
a>=b is second
long hawk
In any case, we just get y ≤ x.
So, now draw both of those regions on the same plane.
And then you'll see what integer points lie in the resulting region.
mild topaz
srry
mild topaz
thank u very much bro
long hawk
thank u very much bro
Should be a^2 + b^2, not (a + b)^2.
mild topaz
but answer is 9 bro
long hawk
but answer is 9 bro
Why only four terms? There are five points.
mild topaz
Why only four terms? There are five points.
but last one is 0,0 which is 0?
long hawk
but last one is 0,0 which is 0?
Ah, yeah.
In that case you made a mistake in one of the terms.
The numbers we have are 0, 1, 2, 1 + i and 1 - i.
mild topaz
thank u very much bro
how to say thank u in this server can u guide i m new here
+close
lilac narwhalBOT
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