Solve the equation $$\(z^{2}-2 p \mathrm{iz} z-q=0\)$$, where $$\(p\)$$ and $$\(q\)$$ are real constants. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_31 Year：2021 Question No：5(a)
Answer:
Use quadratic formula and \(i^{2}=-1\)
Obtain answers \(p \mathrm{i}+\sqrt{q-p^{2}}\) and \(p \mathrm{i}-\sqrt{q-p^{2}}\)
Obtain answers \(p \mathrm{i}+\sqrt{q-p^{2}}\) and \(p \mathrm{i}-\sqrt{q-p^{2}}\)
Knowledge points:
3.9.3 use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs (e.g. in solving a cubic or quartic equation where one complex root is given.)
Solution:
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