Multiplying a non-zero complex number by \( \frac{1 - i}{1 + i} \) results in a rotation about the origin on an Argand diagram - HSC - SSCE Mathematics Extension 2 - Question 5 - 2016 - Paper 1
Question 5
Multiplying a non-zero complex number by \( \frac{1 - i}{1 + i} \) results in a rotation about the origin on an Argand diagram.
What is the rotation?
(A) Clockwise... show full transcript
Worked Solution & Example Answer:Multiplying a non-zero complex number by \( \frac{1 - i}{1 + i} \) results in a rotation about the origin on an Argand diagram - HSC - SSCE Mathematics Extension 2 - Question 5 - 2016 - Paper 1
Step 1
Simplify the complex number
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Answer
To understand the effect of multiplying by ( \frac{1 - i}{1 + i} ), we first simplify this expression. We can multiply the numerator and denominator by the conjugate of the denominator:
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Answer
The complex number (-i) can be represented on the Argand diagram as making an angle of (-\frac{\pi}{2}) radians, which corresponds to a rotation of \frac{\pi}{2}) radians in a clockwise direction.
Step 3
Conclusion
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Answer
Therefore, multiplying by ( \frac{1 - i}{1 + i} ) results in a rotation of ( \frac{\pi}{2} ) radians clockwise. The correct option is (B) Clockwise by ( \frac{\pi}{2} ).
