Given instead that triangle $$\(O A B\)$$ is equilateral, express $$\(q\)$$ in terms of $$\(p\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_31 Year：2021 Question No：5(c)
Answer:
Carry out a correct method for finding a relation, e.g. use the fact that the argument of one of the roots is \((\pm) 60^{\circ}\)
State a correct relation in any form, e.g. \(\frac{p}{\sqrt{q-p^{2}}}=(\pm) \sqrt{3}\)
Simplify to \(q=\frac{4}{3} p^{2}\)
Alternative method for Question \(5(c)\)
Carry out a correct method for finding a relation, e.g. use the fact that the sides have equal length
State a correct relation in any form, e.g. \(4\left(q-p^{2}\right)=p^{2}+q-p^{2}\)
Simplify to \(q=\frac{4}{3} p^{2}\)
State a correct relation in any form, e.g. \(\frac{p}{\sqrt{q-p^{2}}}=(\pm) \sqrt{3}\)
Simplify to \(q=\frac{4}{3} p^{2}\)
Alternative method for Question \(5(c)\)
Carry out a correct method for finding a relation, e.g. use the fact that the sides have equal length
State a correct relation in any form, e.g. \(4\left(q-p^{2}\right)=p^{2}+q-p^{2}\)
Simplify to \(q=\frac{4}{3} p^{2}\)
Knowledge points:
3.9.1 understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal
3.9.4 represent complex numbers geometrically by means of an Argand diagram
Solution:
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