CAIE A-Level Mathematics A2 3.9.6 Complex Numbers Questions
Practise finding square roots of complex numbers in Cartesian and polar forms and solving related equations.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- find square roots of complex numbers in Cartesian form
- use modulus and argument to express complex square roots
- solve quadratic equations involving complex numbers
CAIE A-Level Mathematics A2 3.9.6 Complex Numbers Questions question 1
[Maximum number: 5]
The square roots of 24-7i can be expressed in the Cartesian form x+i y, where x and y are real and exact.
By first forming a quartic equation in x or y, find the square roots of 24-7 i in exact Cartesian form.
Square x+i y obtaining three terms when simplified and equate real
and imaginary parts to 24 and -7 respectively
Having used i^2=-1.
Obtain equations x^2-y^2=24 and 2 x y=-7
Marking guidance:
Allow 2 x y i=-7 i.
Eliminate one variable by correct method and find a horizontal equation in the other
All powers of x or y are positive and are in the numerator.
Obtain 4 x^4-96 x^2-49=0 or 4 y^4+96 y^2-49=0
or 3-term equivalents
Obtain answers 7 22-22 i and -7 22+22 i or exact equivalents
and no others
E.g. +/-(7 22-22 i), but not +/-(7 22 22 i) or
( +/- 7 22 22 i).
Allow coordinates or x=, y= paired correctly. ISW converting to different form.
Must simplify 49.
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