2019 RI P1 Q7
2019 RI P1 Q7
10 marks
Prelims
- The complex numbers \(3+2\mathrm{i}\), \(z\), \(4-6\mathrm{i}\) are the first three terms in a geometric progression. Without using a calculator, find the two possible values of \(z\).[4]
- The complex number \(w\) is such that \(w=a+b\mathrm{i}\), where \(a\) and \(b\) bare non-zero real numbers. The complex conjugate of \(w\) is denoted by \(w^*\). Given that \(\frac{{{w}^{2}}}{w^*}\) is a real number, find the possible values of \(w\) in terms of \(a\) only.[4]
- Hence, find the exact possible arguments of \(w\) if \(a\) is positive.[2]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a)\(-5+\mathrm{i}\)or \(5-\mathrm{i}\)(b)(i) \(w=a+\mathrm{i}a\sqrt{3}\)or \(w=a-\mathrm{i}a\sqrt{3}\), \(b=a\sqrt{3}\)or \(-a\sqrt{3}\) (ii) arg\((w)=\frac{\pi }{3}\)or arg\((w)=-\frac{\pi }{3}\)
Need help? Join our JC Math tuition classes.
Learn more