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Solved assignment for complex number
Typology: Assignments
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1.Question: The value of the sum where equals Options: (a) (b) (c) (d) 0 Answer: (b) Solution: Sum of any 4k consecutive pounds of i is 0 2.Question: The sequence upto 100 terms simplifies to where Options: (a) (b) (c) (d) Answer: (a) Solution: 3.Question: Let The product of the real part of the roots of is Options: (a) (b) (c)
(d) Answer: (b) Solution: or are 3 and - 4.Question: If and are such that then Options: (a) (b) (c) (d) Answer: (b) Solution: 5.Question: The inequality represents the following region Options: (a)
8.Question: The curve represented by is Options: (a) a parabola (b) an ellipse (c) a circle (d) a rectangular hyperbola Answer: (d) Solution: 9.Question: Real part of is Options: (a) (b) (c) (d) Answer: (a) Solution: 10.Question: Let z and are two non-zero complex numbers such that and then z equal to Options: (a) (b) (c) (d) Answer: (d) Solution: Let
11.Question: Number of values of x (real or complex) simultaneously satisfying the system of equations and is Options: (a) 1 (b) 2 (c) 3 (d) 4 Answer: (a) Solution: are 18th^ roots of unity except 1 are 14th^ roots of unity except 1 common roots When K = 7 And m = 9 12.Question: If and then the value of is equal to Options: (a) 2 (b) 3 (c) 4 (d) 6 Answer: (a) Solution: Given 13.Question: A point ‘z’ moves on the curve in an argand plane. The maximum and minimum values of are Options: (a) 2, 1 (b) 6, 5 (c) 4, 3
16.Question: If then is equal to: Options: (a) (b) (c) (d) Answer: (c) Solution: 17.Question: The set of points on an Argand diagram which satisfy both are lying on Options: (a) a circle and a line (b) a radius of a circle (c) a sector of a circle (d) an infinite part line Answer: (c) Solution:
18.Question: If then the locus of z is Options: (a) (b) (c) (d) Answer: (a) Solution: a ray starting form (2, 3) and making with +ve x-axis 19.Question: The origin and the roots of the equation form an equilateral triangle if Options: (a) (b) (c) (d) Answer: (c) Solution: ( from equilateral triangle)
22.Question: If z and are two non-zero complex numbers such that then is equal to- Options: (a) 1 (b) - (c) (d) Answer: (d) Solution: 23.Question: For two complex numbers if Options: (a) (b) (c) (d) Answer: (a) (d) Solution: either or
24.Question: Which of the following, locii of z on the complex plane represents a pair of straight lines? Options: (a) (b) (c) (d) Answer: (a) (b) Solution: is bisector line 25.Question: If the complex numbers represents vertices of an equilateral triangle such that then which of the following is correct? Options: (a) (b) (c) (d) Answer: (b) (c) (d) Solution: Centroid is origin 26.Question: If S be the set of real values of x satisfying the inequality then S contains- Options: (a)
(d) Answer: (a) (b) (d) Solution: 29.Question: Value(s) of is/are- Options: (a) (b) (c) (d) Answer: (a) (c) Solution: 30.Question: If centre of ABCD is at z = 0. If affix of vertex A is centroid of triangle ABC is/are- Options: (a) (b) (c) (d)
Answer: (c) (d) Solution: Centroid 31.Question: If is an imaginary cube root of unity, then a root of equation can be- Options: (a) (b) (c) (d) Answer: (d) Solution: or or only
Options: (a) 1 (b) (c) (d) Answer: (b) (c) Solution: Clearly satisfy above equation Also satisfies 4.Question: If for then- Options: (a) (b) (c) (d) Answer: (a) (d) Solution: 5.Question: Let two complex numbers represented by points on the circle and respectively, then- Options: (a) (b)
(c) (d) None of these Answer: (a) (b) (c) Solution: lies on and Also lies on (diameter) 6.Question: If be any two complex numbers such that then which of the following may be true- Options: (a) (b) (c) (d) Answer: (a) (b) (c) (d) Solution: or 7.Question: Let represent three vertices of where is cube root unity, then- Options: (a) centroid of is
9.Question: Let z and are two complex numbers such that and then z equals- Options: (a) 1 or i (b) i or -i (c) 1 or - (d) I or - Answer: (c) Solution: Let lies on bisectors of lies on real axis can be only 10.Question: If are two polynomials such that the polynomial is divisible by then- Options: (a) (b) (c) (d) Answer: (a) (c) (d) Solution:
