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How do you find the maximum value of a complex number?
1 Answer
- Let z=r(cosθ+isinθ)
- z−1=r−1(cosθ−isinθ)
- |z+1z|=|(r+1/r)cosθ+(r−1/r)isinθ|
- (r2+1/r2)+2cos2θ=a2.
- ⇒x2+1=x(a2−2cos2θ)
- ⇒x2−x(a2−2cos2θ)+1=0.
What is the minimum value of 2z 1 3z 2 where z is a complex number?
The given answer is 1/3. So Minimum value is 13.
How do you find the minimum value by completing the square?
Starts here3:29The Minimum Value Of A Quadratic By Completing The Square (-p,q)YouTube
In which quadrant does the complex number lie?
We know that the x-axis on the complex number plane represents the real number line and y-axis represents the imaginary number line. So, a complex number with negative real part and positive imaginary part will lie in the second quadrant in the complex plane.
What is the minimum value of |Z-1|+|Z-5|?
So |z-1| is the length of the line segment joining z and 1. We need to find the minimum value of |z-1|+|z-5|, i.e., sum of distances of z from 1 and 5. It is minimum, if z is the midpoint, of 1 and 5. Hence z= (1+5)/2=3, and the answer is 4. Edit: z need not be the mid-point. The minimum is the distance between the points, which is 4.
Are Z1 and Z2 the same?
It means that (z1/z2) =R, some real number. Ok, so this is proved and it seems that z1 and z2 are the same except for a factor. Geometrically, Origin, z1, z2 are collinear. When we are given two complex numbers, we can form a triangle from Origin to z1 to z2 to Origin.
What is the minimum distance when P lies on the x axis?
The distance would be minimum when P lies on the X axis between the points (1,0) and (3,0) . The minimum distance would be equal to the distance between (1,0) and (3,0) which is 2. Was this answer helpful?
How do you prove that complex numbers lie on a line?
In fact what we have done is to prove that statement. If the complex numbers lie on a line, they can be written as where and Again the expression would be minimized by for some complex number lying in the same line, i.e., of the form and the expression will become and the previous argument applies. The 4 Worst Blood Pressure Drugs.