Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $\left(\frac{3}{2}+\frac{\sqrt{3}}{2} i \right)^{50}=3^{25}(x+ i y)$, then $x^2+y^2=$
A
$-1$
✓
1
C
$0$
D
None of these
✓
Answer
Correct option: B.
1
(B) $\left(\frac{3}{2}+ i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+ i y)$ Taking modulus on both sides, we get $\left(\sqrt{\frac{9}{4}+\frac{3}{4}}\right)^{50}=3^{25} \sqrt{x^2+y^2}$ $\Rightarrow(\sqrt{3})^{50}=3^{25} \sqrt{x^2+y^2} \Rightarrow 1=\sqrt{x^2+y^2}$ $\Rightarrow x^2+y^2=1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.