Start the test Question no. 1 Suppose, ω and ω 2 are two distinct cube roots of unity different from 1. Then, what is (ω 1 - ω 2 ) 2 equal to? 3   1   -1   -3 Question no. 2 What is the argument of the complex number (−1 − i) , where i = √(−1)?   5π/4   -5π/4   3π/4 None of these Question no. 3 What is one of the square roots of 3 + 4i, where i = √(−1)? 2+i   2-i   -2 + i   -3 - i Question no. 4 Consider the following statements I. ( ω 10 +1) 7 + ω = 0 II. ( ω 105 +1) 10 = p 10 for some prime number p, where, ω ≠ 1 is a cubic root of unity. Which of the above statement(s) is/are correct? Only I   Only II   Both I and II   Neither I nor II Question no. 5 The origin and the roots of the equation z 2 + pz + q = 0 form an equilateral triangle, if p 2 = q ...

Practice question For Complex Number 1.If w is a complex cube root of unity and x 2 = w 2 - w -2 , then what is the value of x 2 + 4x + 7 ? 2. If z is complex number such that z + z -1 = 1 , then what is the of z 99 + z -99 ? 3. If the point z 1 = 1 + i is the reflection of the point z 2 in the line i z - iz = 5 , what is the point z 2 ? 4. What is the real part of (sinx + icosx) 3 ? 5. If x = a + b , y = aα + bβ , z = aβ + bα , where α and β are complex cube root of unity , then show that xyz = a 3 + b 3 . 6. Let z be the complex number such that |z| + z = 3 + i , what is the value of |z| ? 7. Find the condition for which the complex number sinx + icos2x and cosx - isin2x are conjugate to each other ? 8. For all complex number z 1 , z 2 , satisfying |z 1 | = 12 and |z 2 - 3- 4i | = 5 , what is the minimum value of |z 1 - z 2 | ? 9. If iz 3 + z 2 -z + i = 0 , then show that |z| = 1. 10. If z 1 and z 2 are two non...

Active And Passive Voice Question no. 1 Sachin answered my questions. looks_one My questions were answered by Sachin. looks_two My questions had answered by Sachin. looks_3 My questions had been answered by Sachin. looks_4 My questions were being answered by Sachin. Question no. 2 Everybody supported the proposal. looks_one The proposal had supported by everybody. looks_two The proposal had been supported by everybody. looks_3 The proposal was supported by everybody. looks_4 None of these Question no. 3 What happened proved my point. looks_one My point had proved by what happened. looks_two My point were proved by what happened. looks_3 My point had been proved by what happened. looks_4 My point was proved by what happened. Question no. 4 Your medicine firm represents the union. looks_one The union is represented by your medicine firm. looks_two The union was represented by your medicine firm...

Vector Question no. 16 If a , b and c are three coplanar vector , then looks_one a .( b ✕ c )=1 looks_two a .( b ✕ c )= 3 looks_3 c .( a ✕ b )=0 looks_4 b .( c ✕ a )=1 Answer Option looks_3 c .( a ✕ b )=0 Solution Solution : If a , b and c are three coplanar vector c .( a ✕ b )=0 Question no. 17 Given a = i + j - k and b= - i + 2 j + k , c= - i + 2 j - k . A unit vector prependicular to both a + b and c + b looks_one i looks_two j looks_3 k looks_4 ( i + j + k )/√3 Answer Option looks_3 k Solution Solution : a = i + j - k b= - i + 2 j + k c= - i + 2 j - k a + b = 3 j c + b = -2 i + 4 j A unit vector prependicular to both a + b and c + b is cross product of both vector. Unit Vector = k Question no. 18 For any vector a and b ,if a ✕ b =0 and a . b =0 then looks_one a is parallel to...