@wibawamaths: If you always find yourself spending too much time on Complex Numbers with Trigonometry questions, Then you NEED this heuristic. Factorising half the argument out of a complex number written in Euler form works 99% of the time. BONUS INSIGHT: More generally, the parent heuristic is to factorise the ARITHMETIC MEAN of the arguments, from the sum of exponential forms with equal moduli. That’s why for 1 ± eⁱᶿ = eⁱ⁰ ± eⁱᶿ, We factorise eⁱᶿᐟ² because that has the average argument between 0 and θ. I encourage you to try it yourself with more general arguments, You’ll see it fall into place in a similar fashion as expected. I teach heuristics like this to potential state-ranking students in all my classes, So join my Top Achievers Class of 2024 at Proficiency Education with the LINK IN BIO 🔗... If you’re serious about Year 12 4U maths! #hsc #math #nesa #sydneystudent #mathtutor #mathclass

William Wibawa | HSC Maths

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Wednesday 10 January 2024 10:01:46 GMT