Mathematics for JEE Main and Advanced
Complex Numbers
Complex numbers drawn on the Argand plane: modulus, argument, rotation and locus, one idea per lesson.
Modulus and Argument of a Complex Number
A complex number is a point, and also an arrow from the origin. Its modulus is how long the arrow is. Its argument is which way the arrow points.
Coming on Sunday, 11 October at 5 PM IST
The video and its free notes come out together.
Modulus and Argument of a Complex Number
A complex number is a point, and also an arrow from the origin. Its modulus is how long the arrow is. Its argument is which way the arrow points.
Free PDF, 5 pages: the idea, a solved example, practice questions with answers.
Multiplication of Complex Numbers as Rotation
Multiplying by a complex number w turns the arrow by arg w and scales its length by |w|. The lengths multiply and the angles add, so one multiplication can rotate any point about the origin.
Coming on Wednesday, 14 October at 5 PM IST
The video and its free notes come out together.
Multiplication of Complex Numbers as Rotation
Multiplying by a complex number w turns the arrow by arg w and scales its length by |w|. The lengths multiply and the angles add, so one multiplication can rotate any point about the origin.
Free PDF, 6 pages: the idea, a solved example, practice questions with answers.
Rotation Theorem in Complex Numbers
To rotate a point about any centre, shift the centre to the origin, turn by multiplying, and shift back. On a triangle, the same idea gives the rotation theorem.
Coming on Sunday, 18 October at 5 PM IST
The video and its free notes come out together.
Rotation Theorem in Complex Numbers
To rotate a point about any centre, shift the centre to the origin, turn by multiplying, and shift back. On a triangle, the same idea gives the rotation theorem.
Free PDF, 7 pages: the idea, a solved example, practice questions with answers.
More lessons are on the way
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