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## Algebra (all content)

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

Lesson 11: Challenging complex number problems

# Challenging complex numbers problem: complex determinant

Paper 1 Problem 53 from the challenging 2010 IIT JEE exam, about determinant of a complex numbers matrix. Created by Sal Khan.

## Want to join the conversation?

• At the end of the video, Sal says that the number of complex numbers that satisfy the solution of z is 1. The only solution is 0, and 0 is not a complex number, so why is there 1 complex number that satisfies the solution of z?
• Sal means "complex number" in the more general sense which includes pure real numbers (and pure imaginary numbers) as also being complex. Actually, unless someone is being really specific, they will always mean "complex number" in that sense from this point forward.
• When calculating the determinate why did he only use the first row?
• We can use any row or column for calculating the determinant. He just randomly used the first row.
• At , how come w^4 isn't equal to w^2^2 (since w^6 is w^3^2)? 😮
• w^4 is equal to w^2^2 if you happen to square the w^2 's value you would get same value as the one calculated by Sal.
• I don't understand why he said the determinant should be equal to zero, and then calculate the determinant, rather than just solving this matrix as you do for an homogeneous system of equations = 0 ?
(1 vote)
• Notice that the matrix has straight vertical bars on the side | | rather than the brackets [ ] that usually signify a matrix. The vertical lines tell us that this is a determinant.
• At he says that z=0 is the only solution but the complex no. is 1.How?
(1 vote)
• He says z=0 is the only solution for the equation and number of solutions for the equation is 1 since only z=0 satisfies the equation
• Was that a fast fourier transform matrix?
• Yes Sal, please make a video on this if you haven't already!
(1 vote)
• I don't understand how Sal used the determinant chart. Can anyone help me?
(1 vote)
• In a problem, when the value of a matrix is set to a constant, is it automatically assumed the problem is asking for the determinant of the matrix? I was a bit confused when Sal started finding the determinant of the matrix.
(1 vote)
• how did you get the height to be sq (3)/2 and base to be -0.5??
(1 vote)
• At Why did you swap signs sir?
(1 vote)