complex number z, Mathematics

Assignment Help:

For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..?

Solution) |z| + |z-(e^ia)| + |z-2(e^ia)|

we see.....oigin , e^ia , 2e^ia ,  forms a straight line.

and for minimum value..... z must coincide with e^ia

hence the equation becomes:

=|e^ia| + 0 + |-e^ia|

=1 + 0 + 1

=2(ANS)


Related Discussions:- complex number z

Geometry, how you know that your first quadrilateral is an isosceles trapez...

how you know that your first quadrilateral is an isosceles trapezoid

Find inverse laplace transform, Question: Find Inverse Laplace Transfor...

Question: Find Inverse Laplace Transform of the following (a) F(s) = (s-1)/(2s 2 +8s+13)     (b) F(s)= e -4s /(s 2 +1) + (1/s 3 )

Estimate how much work is completed in stretching, A spring has a natural l...

A spring has a natural length of 20 Centimeter. A 40 N force is needed to stretch and hold the spring to a length of 30 Centimeter. How much work is completed in stretching the spr

Calculus, how to find relative extrema at the indicated interval of the fol...

how to find relative extrema at the indicated interval of the following functions and how to sketch it?

Trigonometry, if theta is a positive acute angle and 2sin theta +15cos squ...

if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta

Demerits and merit-the geometric mean , The geometric mean Merits ...

The geometric mean Merits i.  This makes use of all the values described except while x = 0 or negative ii.   This is the best measure for industrial increase rates

Find the interval of validity, Solve the subsequent IVP and find the interv...

Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 ,       y(2) = - 1,  x > 0 Solution Thus, the first thing that we re

Dynamical system and differential equations, 1. Discuss lyapunov function t...

1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd