2023HSCShort answer

Q11 (a)

2 marks

Question

Solve the quadratic equation $z^2-3z+4=0$ , where $z$ is a complex number. Give your answers in Cartesian form.

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Completes the square<br>OR<br>Uses quadratic formula	1

Sample answer:

$z=\frac{3\pm\sqrt{9-16}}{2}$
$=\frac{3\pm\sqrt{-7}}{2}$
$=\frac{3}{2}\pm\frac{\sqrt7}{2}i$

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.

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