Academia Aeternum
तमसो मा ज्योतिर्गमय
From i²=−1 to the Argand Plane — All 52 NCERT Solutions Explained
2 exercise files · 28 total questions
\(i^{4k}=1,\; i^{4k+1}=i,\; i^{4k+2}=-1,\; i^{4k+3}=-i\)\(|z| = \sqrt{a^2 + b^2}\)\(z^{-1} = \dfrac{\bar{z}}{|z|^2}\)\(z = r(\cos\theta + i\sin\theta)\)\(D < 0:\; \text{roots} = \dfrac{-b \pm i\sqrt{|D|}}{2a}\)Step 1 — Division: multiply top and bottom by conjugate of denominator (a−bi). Step 2 — Argument: compute arctan(b/a) then adjust for quadrant using signs of a,b. Step 3 — Quadratic: compute D; if D<0 write √(−|D|)=i√|D| and proceed normally. Step 4 — Powers of i: divide exponent by 4; use the remainder.
Get in Touch
Questions, feedback, or suggestions?
We'd love to hear from you.