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## Algebra (all content)

### Course: Algebra (all content)>Unit 16

Lesson 11: Challenging complex number problems

# Challenging complex numbers problem (1 of 3)

Paper 1 Problem 39 from the challenging 2010 IIT JEE exam, about complex numbers. Created by Sal Khan.

## Want to join the conversation?

• Hey Sal, first of all, nice video. The problem is, we're not given this much time while solving the questions in the exam. Any tips on how to solve such questions in a quicker span of time? Thank you :)
• Three tips on that: practice, practice and practice.
• What does the argument of z mean? I probably missed it somewhere.
• z means any complex number of the convex combination of z1 and z2
(1 vote)
• The question was MCQ. How can there be more than one possible answer?
(1 vote)
• in your IIT JEE exam you also get MCQ's with more than one option right
they are just given to confuse students and you are supposed to mark all the right answers...
• what is demoiveres theorem
• demoiveres theorem states that for any complex number (and, in particular, for any real number) x and integer n it holds that (cos x + i sin x)^n = cos(nx) + i*sin(nx), where i=sqrt(-1).
• i really love all the videos ...but hello there!... this is epic IIT JEE exam , in real exam you do not have this much time to solve question in depth. if only u can solve this question in few seconds ?
• well if u want to take this exam the best way to solve this type of questions is to keep practicing
• at the absolute value of 1-t... wouldn't that be 1+t because it's the absolute value of it. I know it is ultimately positive, but there is a minus sign?
(1 vote)
• absolute function is defined as follows:
IxI= +x when x>0
IxI= -x when x<0
here as 0<t<1, 1-t will be positive, so modulus of 1-t will be +(1-t)= 1-t
modulus does not simply mean changing negative to positive, abs(1-t) will give + or - sign to the whole term and not just 't'. had (1-t) been negative, absolute value would have been -(1-t)= -1+t..remember this!
• Hello, i was wondering what magnitude means? Is there a video that I might have skipped? Thanks :)
• magnitude is just the absolute value of a number
if you have a -3 then the magnitude of this quantity is 3
here you are just ignoring the direction....
• Why is D incorrect?
(1 vote)
• D isn't incorrect. In the next video Sal explains why choice B is incorrect, but then (from about ) goes on to use that same reasoning to show that choice D is correct.