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1. ### Format for Mathematical Induction proofs <3

Don't forget, sometimes, the base case maybe for, say, n = 3 instead of 1.
2. ### 1141 with only MX1

Will they allow you to take 1141 with just your MX1? If so, I can help you learn 1141 contents during your December/January break after your HSC, so that you won't be badly handicapped. But you must be pretty good in your MX1.
3. ### binomials help ;/

Nicely set out. Your 'x' looks like an 'n'. Computationally, easier this way. \therefore \binom {15} {10} 5^5 (2x)^{10} = \binom {15}{11}5^4 (2x)^{11}\\ \\ \therefore \frac {(2x)^{11}}{(2x)^{10}} = \frac {\binom {15}{10} 5^5}{\binom {15}{11}5^4} \\ \\ \therefore 2x = \frac {15! \times 11!4...
4. ### Complex Q

z^5 + a = 0 is a polynomial equation (of degree 5) whose roots are the points on the circle. Since these points are symmetric about the x-axis, it means every (of the 4) complex roots appear in complex-conjugate pairs. Therefore the coeffs of this polynomial eqn must be all reals; therefore 'a'...
5. ### Complex Q

i.e |z - 0| = |z -(1+i)| It means the distances of (all) z from the points O(0,0) and from A(1,1) are equal. So the equation defines the locus of a point which is equidistant from these 2 given points O & A, viz. the perpendicular bisector of the line segment OA. Draw this perpendicular...

20. ### trig inequality

\therefore tan^2x + tan x -6 < 0\\ \\ \therefore (tan x + 3)(tan x - 2) < 0 \\ \\ \therefore -3 < tan x < 2