IIT JEE complex numbers (part 1) | Imaginary and complex numbers | Precalculus | Khan Academy

2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 1)

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[rockingosh]

i love u guys... u just simplified complex numbers so much.. thank u MUCH... i love u guys... god bless u peeps!

[justinebiju]

Sir can we approach the problem taking z, z1 and z2 as vectors:
Given,
z=(1-t)z1+tz2
=z1+t(z2-z1)
Which is the general equation of a line containing points z1 and z2. But since 0<t<1, locus of z becomes a line segment joining two points z1 and z2(excluding z1 and z2).Hence z is any point on the line segment.
Since |z-z1| is the distance of z1 from z.
Taking points A(z1), B(z2), C(z).
AC+CB=AB :-option [A] is correct
Taking z-z1 being a vector pointing from point z1 to z and and taking Arg(z-z1) as the vector's direction ratios we get option [D].
Option [C] can also be obtained by taking a.b=|a||b|cosA and solving the matrix since |z-z1|=|conj(z)-conj(z1)|

[MauMoralesMMS]

The pace is good, please don't change your style

[bazzingalore]

Really good! But since these are higher level problems, could you explain the shorter steps faster? Most people preparing for IIT are very familiar with the basics, so could you just explain the hard bit and not the whole thing in detail? =)

[pranav]

But hey we get only around 2 minutes to solve the questions in IIT-JEE !!

[kishorekumarsathishkumar]

im writing this exam in 3 years and this is scary

[rockingosh]

i love u guys... u just simplified complex numbers so much.. thank u MUCH... i love u guys... god bless u peeps!