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If the complex numbers z1,z2,z3 represents vertices of an equilateral triangle such that z1=z2=z3, then which of following is correct?

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Important Questions on Complex Numbers

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 14
If S be the set of real values of x satisfying the inequality 1-log2|x+1+2i|-22-1≥0, then S contains
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 15
If ampz1z2=0 and z1=z2=1, then
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 16
If the vertices of an equilateral triangle are situated at z=0,z=z1,z=z2, then which of the following is/are true -
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 17
Value(s) of (-i)13 is/are -
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 18
Centre of square ABCD is at z=0. If affix of vertex A is z1, centroid of triangle ABC can be:
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 19
If ω is an imaginary cube root of unity, then a root of equation x+1ωω2ωx+ω21ω21x+2=0, can be
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 11
Let z1 and z2 be two complex numbers such that z1-2z22-z1z¯2=1 and z2≠1, find z1.
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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 12
Let A=a∈R∣ the equation (1+2i)x3-2(3+i)x2+(5-4i)x+2a2=0 has at least one real root}. Find the value of 15∑a∈Aa2.