02%20-%20Complex%20Numbers

02%20-%20Complex%20Numbers - 02 - COMPLEX NUMBERS Page 1 (...

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Unformatted text preview: 02 - COMPLEX NUMBERS Page 1 ( Answers at the end of all questions ) ( 1 ) If the cube roots of unity are 1, , 2 , then the roots of the equation ( x - 1 ) 3 + 8 = 0 are ( a ) - 1, - 1 + 2 , - 1 - 2 2 ( b ) - 1, - 1, - 1, ( c ) - 1, 1 - 2 , 1 - 2 2 ( d ) - 1, 1 + 2 , 1 + 2 2 [ AIEEE 2005 ] ( 2 ) If z 1 and z 2 are two non-zero complex numbers such that l z 1 + z 2 l = l z 1 l + l z 2 l, then arg z 1- arg z 2 is equal to ( a ) 2 ( b ) - ( c ) 0 ( d ) - 2 [ AIEEE 2005 ] ( 3 ) If w = i 3 1 z z- and l w l = 1, then z lies on ( a ) an ellipse ( b ) a circle ( d ) a straight line ( d ) a parabola [ AIEEE 2005 ] ( 4 ) Let z, w be complex numbers such that w i z + = 0 and arg zw = . Then arg z equals ( a ) 4 ( b ) 2 ( c ) 4 3 ( d ) 4 5 [ AIEEE 2004 ] ( 5 ) If z = x - iy and 3 1 z = p + iq, then 2 2 q p q y p x + + is equal to ( a ) 1 ( b ) - 1 ( c ) 2 ( d ) - 2 [ AIEEE 2004 ] ( 6 ) If l z 2- 1 l = l z l 2 + 1, then z lies on ( a ) the real axis ( b ) the imaginary axis ( c ) a circle ( c ) an ellipse [ AIEEE 2004 ] ( 7 ) Let z 1 and z 2 be two roots of the equation z 2 + az + b = 0, z being complex. Further assume that the origin, z 1 and z 2 form an equilateral triangle. Then ( a ) a 2 = b ( b ) a 2 = 2b ( c ) a 2 = 3b ( d ) a 2 = 4b [ AIEEE 2003 ] 02 - COMPLEX NUMBERS Page 2 ( Answers at the end of all questions ) ( 8 ) If z and w are two non-zero complex numbers such that l zw l = 1 and Arg ( z ) - Arg ( w ) = 2 , then w z is equal to ( a ) 1 ( b ) - 1 ( c ) i ( d ) - i [ AIEEE 2003 ] ( 9 ) If x i 1 i 1 +- = 1, then the value of smallest positive integer n is given by ( a ) x = 4n ( b ) x = 2n ( c ) x = 4n + 1 ( d ) x = 2n + 1 [ AIEEE 2003 ] ( 10 ) If 1, , 2 are the cube roots of unity, then the value of = n 2n 2n n 2n 1 1 1 is ( a ) 1 ( b ) 0 ( c ) ( d ) 2 [ AIEEE 2003 ] ( 11 ) If i c i c- + = a ib, where a, b, c are real, then the value of a 2 + b 2 is ( a ) 1 ( b ) - 1 ( c ) c 2 ( d ) - c 2 [ AIEEE 2002 ] ( 12 ) If z = x + iy, then l 3z - 1 l = 3 l z - 2 l represents ( a ) x-axis ( b ) y-axis ( c ) a circle ( d ) line parallel to y-axis [ AIEEE 2002 ] ( 13 ) If the cube roots of unity are 1,...
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02%20-%20Complex%20Numbers - 02 - COMPLEX NUMBERS Page 1 (...

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