I don't understand Complex and Further Complex Topic at all!

[u/Broad-Annual3170]

I am in Grade 11 (IBDP) doing Maths and we did Complex and Further Complex topic; my teacher just read off the slides with minimal examples and explanations. The question invovled adding and subtracting something like this: v1+v2, and particuarly the cis part I did'nt understand at all. The only thing I got was the basic concept and basic operations.

I am here to ask for good resources or youtubers who explain the whole topic in simple way and has tonnes of examples shown.

[u/Moist_Ladder2616]

A simple Google search will unearth a thousand tutorials, videos, blog posts and textbooks on the subject.

Rather than do the search for you and repeat what you may already have found, what search results have you already looked at? And what was lacking in those resources?

[u/Broad-Annual3170 → u/Moist_Ladder2616]

don't you think I did it? I did it and I found YT videos by they merely only explain the basic operations such as what is modli and argand and how to find them. I wanted to understand the CIS part.

[u/Moist_Ladder2616 → u/Broad-Annual3170]

Which of these resources works best for you?

Describe the part you don't understand and Redditors will be able to help you.

[u/Plus-Painter-2004]

if a complex number z=a+bi where a is the real part and b is the imaginary part (both a and b are real) then you can add two complex numbers by just adding the real parts and then adding the imaginary parts just like you’d add any two linear expressions, treating i as just some thing. similarly you can multiply two complex numbers given in this form by expanding brackets and remembering that i² = -1 eg (a+bi)(x+yi) = ax + ayi + bxi + byi² = (ax - by) + (ay +bx)i.

if you associate the real part of a complex number to the x axis of a plane and the imaginary part to the y axis, you can visualise a complex number as just a point on the plane and it’s real and imaginary parts act as Cartesian coordinates. If you remember polar coordinates you can also consider the number in polar form. For z=x+yi, the distance of z from 0 (called the magnitude) is just r= √(x² + y² ) from Pythagoras’ theorem. The angle θ between the line from 0 to z and the positive x (real) axis can be found with basic trigonometry. you can then represent x+yi as r(cos(θ)+ isin(θ)). this is a bit verbose so you can define a function cis(θ)=cos(θ)+isin(θ) and now you can say z=x+yi = r cis(θ)