A) \[3+4i+i\sqrt{3}(2+3i)\]
B) \[(3+4i)+\frac{1}{\sqrt{3}}\,\,i(2+3i)\]
C) \[(2+3i)+i\sqrt{3}(3+4i)\]
D) \[(2+3i)+\frac{i}{\sqrt{3}}(3+4i)\]
Correct Answer: A
Solution :
\[\frac{z-(1-i)}{AC}=\frac{(2+3i)}{AB}{{e}^{{{i}^{\pi /3}}}}\] |
\[\Rightarrow z-1-i=2\,\,(2+3i)\left( \frac{1}{2}+\frac{\sqrt{3}}{2}i \right)\] |
\[\Rightarrow z-1-i=(2+3i)\,\,(1+\sqrt{3}i)\] |
\[\Rightarrow z=3+4i+i\sqrt{3}(2+3i)\] |
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