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2022 Mathematics Extension 2 Q11 (b) (ii) | HSC Atlas

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2022TrialShort answer

Q11 (b) (ii)

2 marks

Question

Hence solve the equation $z^2-3iz-(4+6i)=0$ .

Try the question before revealing the answer.

Solution

$z=\frac{3i\pm\sqrt{(-3i)^2-4(-4-6i)}}{2}$

$=\frac{3i\pm\sqrt{7+24i}}{2}$

$z=2+3i\quad\text{or}\quad z=-2$

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Complex Numbers

Solving equations with complex numbersUse De Moivre's theorem and solve equations and polynomial problems involving complex and conjugate roots.

Source

Girraween 2022 4U Trial PaperGirraweenQuestion paper page 6Guidance page 14View original source ↗

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