2022TrialShort answer

Q11 (b) (i)

3 marks

Question

By letting $(x+iy)^2=7+24i$ , where $x,y$ are real, find $\sqrt{7+24i}$ in Cartesian form.

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Solution

$x^2-y^2=7,\qquad 2xy=24$

$y=\frac{12}{x}$

$x^4-7x^2-144=0$

$x^2=16\text{ or }-9$

$x=\pm4,\qquad y=\pm3$

$\sqrt{7+24i}=\pm(4+3i)$

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Syllabus alignment

Complex Numbers

Arithmetic of complex numbersRepresent and calculate with complex numbers in Cartesian form, including conjugates, division, reciprocals and square roots.

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