6 - Complex Numbers Questions Answers

if one vertex of a triangle having maximum area inscribed ia a circle IZ-iI=5 is 3-3i then find the other two vertices

Asked By: PORURU KRISHNA MOHAN 4 year ago
Maths >> Trigonometry >> Complex Numbers Engineering Exam

what is the angular difference between the +j and -j ?

OR

+4j and -4j  ?

180 degree

if z1=1+i, z2=√3+i , then arg(z1/z2)power50?

Asked By: HARSHITH 6 year ago
The complex number z is such that:|z|=1,z is not equal to -1 and w=z-1/z+1. Then real part of w is:
Asked By: SHEIKH SARTAJ 6 year ago

let z be a complex number satisfying |z-3|=|z-4i|, then find the least possible value of 10|z|.

Asked By: AMIT DAS 7 year ago

In |z-3|=|z-4i|, z represents all points lying on the perpendicular bisector of the line joining 3 and 4i in x-y plane. In this perpendicular bisector, if we draw a perpendicular then it will be the minimum magnitude of z. Construct this as a diagram we will get

sinθ = |z| / (7/8)

or |z| = (7/8)(4/5) = 7/10 The number of roots of equations z15 = 1 and Iarg zI< π/2 is

Asked By: HIMANSHU MITTAL 7 year ago

let z = r(cosθ+i sinθ) and it is given that z15 = 1  =>  r15(cosθ+i sinθ)15 = 1

or r15(cos15θ+i sin15θ) = 1+0i                   (Here we use Demoivre's theorem)

on comparison we get sin 15θ = 0 => 15θ = nπ          here n is an integer

for n = -7 to +7 we will get 15 answers for which θ will lie between -π/2 to +π/2