FINALLY! 4 APPLICATIONS OF COMPLEX NUMBERS IN REAL DAILY LIFE

VISUALIZING MATH 1 (PDF Book Link)

Blog Link

1] How sin( ) is a measure of how much perpendicular two objects/forces are.

2] How cos( ) is a measure of how much parallel two objects/forces are.

3] How in complex numbers
i = rotation by 90 degrees
i^2= rotation by 180 degrees
i^3= rotation by 270 degrees.
i^4 = rotation by 360 degrees.

4] Transpose of a matrix = Rotation by 180 degrees around the diagonal.

5] e^i(angle) = rotation by that angle.

6] sin(30) = 1/2
because at 30 degree the effect of a force reduces to half over the other force/object (as against when the two forces/object are against at 90 degrees w.r.t each other)

7) A X B = |A| |B| sin(angle between A and B).

VISUALIZING MATH 2 PDF BOOK LINK

Visualizing Math 2 deals with concepts like

1) How Fourier Transforms are the side-view of a wave.

2) Laplace Transforms are side-view + front view (Imaginary + real part)

3) How Z Transforms are nothing but the discrete cousin of Laplace and DFT of Fourier.

4) How the number 1 appears actually as a fraction 1/1 in Math which means full of full.

Thus sin(90) = 1/1 = full on influence at 90 deg

Thus Max probability = 1/1 = full of full sample space

Thus cos(0) = 1/1 = full on full influence at 0 deg (when parallel)

Unit Circle radius = 1/1 = magnitude doesn't decrease/increase

throughout the rotation. Else it would have been a ratio like 2/1 or 1/4 etc.

5) How Continous functions can be visualized as those functions which you can draw on a paper without lifting up the pencil.

6) How a function differentiable at a point means if you stand at that point,...

(1) You will experience a slope. Slope will exist.

(2) This slope however will not be infinite. (fully vertical)

(3) The slope will be either towards the left or the right but not both the directions.

(4) The slope will not wriggle like a snake (oscillate ) at that point.

7) How a hermitian matrix can be visualized as a any object which which exhitibits vertical symmetry. So even if it is rotated upside down about the central axis( diagonal of the matrix) you wont be able to tell the difference.

8) How probability can be visualized much more intuitively by multiplying it by 100 and thus converting it into a percentage.

Eg:- a probability of 0.2 can be converted to 0.2 x 100 = 20%

9) How probability density can be understood using an example of the Probability of finding a man after entering New-york v/s finding a man after entering a sparsely populated desert.

And so on.........

The book is still in works and subsequent updated will be sent to your mail id for free.

Binnoy

[Visualizingmathandphysics]

VISUALIZING MATH 1 E-BOOK.

VISUALIZING MATH 2 E-BOOK.

BLOG LINK.

[StarFxPrime]

Man, I want to both give you a hug, and become your friend. Thank you so much for this :)

[manharm]

we knew about rotation even before knowing about complex numbers through 2d geometry. Whats the whole point in using a different number system to represent the known things...?

[kishwarfatima]

May you get great success sir .This channel is just gr8

[pavanjyothiswaroopmangalam]

I feel very good to see this...thanks for everyone's

[singhsstyleofmaths]

Excuse me Sir..., , Kya aapki yeh book mil sakti hai amazon per??? It's really a great way of learning by If yes, , , what's it's cost as per indian rupees???

[baburao]

Thank you so much for making this video

[singhsstyleofmaths]

Really Wonderful and helpful video... Thank you so much Sir 😇💖🌺🙏🙏

[NikhitReddy]

Don't we have the vectors already for that?

[snehagarg]

Sir, direction dikhane k liye i, j, k hai. Ye complex ni hai. Complex itni calculation Jo hai...wo kyun hai ye batayeye

[timesaver]

Sir plz make more videos about real life example I have online vedantu tekegrqm group where 300 active students are there they are looking for some channel who can tell real life examples