A) \[1\pm 2i\]
B) \[i+1\pm \sqrt{3}\]
C) \[2+i(1\pm \sqrt{3})\]
D) \[1+i(1\pm \sqrt{3})\]
E) \[1-i(1\pm \sqrt{3})\]
Correct Answer: D
Solution :
Given, \[z=i\] Let \[{{z}_{1}}+1+i(1\pm \sqrt{3})\] and\[{{z}_{2}}=2+i\] Now, \[|{{z}_{2}}-z|=|2+i-i|\] \[=2\] As we know that the distance from the centre to every vertices is equal. Now, \[|{{z}_{1}}-z|=|1+i(1\pm \sqrt{3})-i|\] \[=|1\pm i\sqrt{3}|=\sqrt{{{1}^{2}}+{{(\sqrt{3})}^{2}}}\] \[=2\] Hence, option (d) is correct.
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