Let z_1 =1+i, z_2 =−1−i and z_3 be complex numbers such that z_1 , z_2 and z_3 form an equilateral triangle. Then z_3 is equal to (A) (√3)(1+i) (B) (√3)(1−i) (C) (√3)(i−1) (D) (√3)(−1−i)


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Question Number 140113 by EnterUsername last updated on 04/May/21

$Let z_{1} = 1 + i, z_{2} = - 1 - i and z_{3} be complex numbers$ $such that z_{1}, z_{2} and z_{3} form an equilateral triangle .$ $Then z_{3} is equal to$ $(A) \sqrt{3} (1 + i) (B) \sqrt{3} (1 - i)$ $(C) \sqrt{3} (i - 1) (D) \sqrt{3} (- 1 - i)$
Commented by mr W last updated on 04/May/21

$z_{3} m u s t b e i n 2^{n d} o r 4^{t h} q u a d r a n t,$ $t h e r e f o r e o n l y (B) i s c o r r e c t .$
Commented by EnterUsername last updated on 04/May/21

$Sir (C) has also been noted as correct answer .$ $How did you get there, please ?$
Commented by mr W last updated on 04/May/21

$i m i s r e a d . (C) i s i n 2^{n d} q u a d r a n t, s o$ $i t i s a l s o c o r r e c t .$
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