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## Algebra (all content)

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

Lesson 11: Challenging complex number problems

# Challenging complex numbers problem (2 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?

• What is IIT JEE?
• its not a tough exam but an exam testing your implementation of theory in a brand new different way you never would have thought. thats why people mostly find it difficult. think before you speak, guys
• What is the difference between magnitude and argument/Arg??
• Seems that a solution for choices A, B and D is overcomplicated, because this problem can be looked at from a 'vectors' point of view.
This is just a linear interpolation between two complex numbers, hence a z (as a point on a complex plane) will always lie on a segment between z1 and z2 (for any 0 < t < 1), so we can make next statements:
1) Choice A tells us that "a distance between z1 and z plus a distance between z and z2 equals a distance between z1 and z2" and that is true, just because point z lies on a segment z1-z2
2) Choice B tells us that a direction (an argument) for (z - z1) and (z - z2) is the same, but that can not be true, because z lies on a line segment z1-z2, therefore this 'vectors' will point in opposite directions.
3) Choice D tells us that a direction (an argument) for (z - z1) and (z2-z1) is the same, and that is true, because z and z2 lie on a same segment and have the same tail.

Am I right? :)
• Thanks for the video, but how will we solve this question without taking options' help?
• WE are verifying if any of the options is correct
so we are MADE to use the options
• What is the 'correct' way of measuring an angle? clockwise or anti-clokwise?
(1 vote)
• Well, in the Cartesian Coordinate Plane, you always measure counter-clockwise unless mentioned otherwise. In angles given in polygons or such, measure the minor angle unless specified otherwise.
• Is this one of the easier questions of the JEE Advanced exam?
(1 vote)
• Kind off. But Still It is one of the Most Difficult Examinations for Engineering Students
• On he multiplied only one siide of argument to -1, is it correct? I mean that it's necessary to multiply both sides.
(1 vote)
• Listen again to the video from to and from to .
In both cases, Sal explains that he is multiplying EACH of TWO factors by -1.
Since -1*-1 = 1, this does not change their value, but simply allows the expression to be written in a different way that helps to solve the problem.