Neco 2022 Further Mathematics Question 48

Practice objective / multiple choice question 48 from the 2022 Neco Further Mathematics examination.

Neco 2022 Further Mathematics Objective / Multiple Choice Hard Difficulty

Question 48 NECO • 2022 • FURTHER_MATHEMATICS • objective

Find all complex numbers \(z\) satisfying \(z^{2}=2z-(1+i)\). Then compute the sum of the reciprocals of the moduli of the solutions.

A. \(\displaystyle \frac{\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}}{\sqrt{2}}\) (approximately \(0.765\))

B. \(\displaystyle \frac{2\sqrt{2+\sqrt{2}}}{\sqrt{2}}\) (approximately \(2.614\))

Correct Answer C. \(\displaystyle \frac{\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}}{\sqrt{2}}\) (approximately \(1.848\))

D. \(\displaystyle \frac{\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}}{2}\) (approximately \(1.307\))

Correct Answer

Correct Option:

\(\displaystyle \frac{\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}}{\sqrt{2}}\) (approximately \(1.848\))

This is Neco 2022 Further Mathematics Question 48. It is one of the objective questions from the 2022 Neco Further Mathematics examination.

Difficulty level: Hard .

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