If $z=\dfrac{\sqrt3}{2}+\dfrac{i}{2}$, find $\left(z^{201}-i\right)^{8}$.
$z=e^{i\pi/6}$, so $z^{12}=1$. Since $201=12\cdot16+9$, $z^{201}=e^{3i\pi/2}=-i$. Then $\left(-2i\right)^{8}=256$.
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If $z=\dfrac{\sqrt3}{2}+\dfrac{i}{2}$, find $\left(z^{201}-i\right)^{8}$.
$z=e^{i\pi/6}$, so $z^{12}=1$. Since $201=12\cdot16+9$, $z^{201}=e^{3i\pi/2}=-i$. Then $\left(-2i\right)^{8}=256$.
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Five-minute concepts: a clear explanation, the definition, key results, a trick and the classic trap.
$|z|=\sqrt{x^2+y^2}$ is the distance of $z$ from $0$.
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Every day at 2 am a new 30-question paper opens: ten questions each in Physics, Chemistry and Mathematics, from easy to hard, written fresh from our course and checked twice. You get 60 minutes and JEE marking (+4 for correct, −1 for wrong). The leaderboard ranks by score and then time, and the top 10 appear on this page. It is open to every student with an account.
Just an account: sign up with your email address or mobile number and a password. Every unit, the daily test, the Sunday full mock, your projected rank and the tutor then open. The tutor answers 20 questions a week, and the count resets every Monday.
Unit 1 of every subject, today’s three concepts (one from each subject, open to everyone until midnight), the daily-test leaderboard and a short 5-question practice set. Everything else opens as soon as you log in.
From the official IIT-JEE, AIEEE, JEE Main and JEE Advanced papers, 1978 to 2026. Each is rewritten in our own words and solved independently; where an official key was disputed, the solution explains the correct mathematics.
Your dashboard turns your Sunday mocks, daily tests and practice into expected marks, then into a JEE Main and JEE Advanced percentile and All-India Rank, shown with a range and a weekly graph. Mocks count most, recent results count more, and the range narrows as you take more tests. It is guidance, not an official prediction. The full method is here.
Every Sunday, every student with an account gets a complete JEE Main paper: 75 fresh questions (25 per subject, 20 single-correct and 5 integer-answer), 3 hours, marked out of 300 with +4 / −1. Your score feeds your projected rank, and answers and full solutions open after midnight.
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