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Question

$$z_{1},\ z_{2},\ z_{3}$$ are vertices of equilateral triangle inscribed in the circle $$|z|=2$$ lf $$z_{1}=1+i\sqrt{3}$$ then $$z_{2}$$ and $$z_{3}$$ are?


A
2,1+i3
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B
2,1i3
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C
2,1i3
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D
2,1i3
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Solution

The correct option is A $$-2,1-i\sqrt{3}$$
$$z_1= 1+i\sqrt3$$
$$z_1 =  2 e^{ i\pi /3 } $$
The other two vertices will lie along the circle rotated by an angle of $$\dfrac{2\pi}{3}$$
Hence, 
$$z_2 = 2e^{i\pi} =-2 $$
$$z_3 = 2e^{5i\pi/3} = 1- i\sqrt{3} $$

Mathematics

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