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Showing posts from May, 2021

Let's complex bash Part 2:P

 Okie so continuing from the previous post ( sorry for huge time gap, got stuck in Allen stuff) A warning though if anyone from the "anti-bash" community is reading, sorry in advance and R.I.P.  Notes:- 1. We have $z_1=r_1e^{i\theta_1}$ and $z_2=r_2e^{i\theta_2}$ then we have $z_1z_2=r_1r_2e^{i(\theta_1+\theta_2)}$ and we get $|z_1z_2|=|z_1||z_2|$ and $\arg z_1z_2=\arg z_1+\arg z_2 .$ SPIRAL SIMILARITIES and TRANSFORMATIONS:- 2. How to rotate a point about origin by 90. If $90^{\circ}$ anti-clockwise then multiply the number by $i$  If $90^{\circ}$ clockwise then multiply by $-i.$ Proof:- Note that $i= 0+1\cdot i.$ So $|i|= \sqrt{0^2+1^2}=1.$ And when we locate $i$ in complex plane, clearly $\arg i=\pi/2.$ Similarly for the second, but note that $\arg -i=-\pi /2.$ (Since angles are measured anti-clockwise) Example:- Here we have $z=1+2i$ then when we multiply $i$ we get $zi=i-2.$ Now, what about we want to dialate a point from one to another and scale it? (Note that that is