Mathematics questions
18011 published questions with worked solutions.
- If i= -1 , then 4+5 (- 12+ i 3 2 )^ 334 +3 (- 12+ i 3 2 )^ 365 is equal to
- ( +i )^4 ( +i )^5 is equal to
- If is a complex number satisfying the equation ^2+ +1=0, then ^ 31 is equal to
- If the expression x2+ x2-i x 1+2i x2 is real then the set of all possible value of x is
- If 1, , ^2 are the cube roots of unity, then (1+ )(1+ ^2)(1+ ^4)(1+ ^8) is equal to
- If is a complex cube root of unity, then 225+(3 +8 ^2)^2+(3 ^2+8 )^2 is equal to
- Let z= +i . Then, the value of _ m=1 ^ 15 Im (z^ 2m-1 ) at =2^ is
- The product of cube roots of -1 is equal to
- If is an imaginary cube root of unity, then (1+ - ^2)^7 equals
- ( -1+ 3i 2 )^ 100 + ( -1- 3i 2 )^ 100 is equal to
- If a= +i , b= +i , c= +i , and bc+ ca+ ab=1, then ( - )+ ( - )+ ( - ) is equal to
- The value of the expression 2 (1+ 1 ) (1+ 1 ^2 )+3 (2+ 1 ) (2+ 1 ^2 )+ +(n+1) (n+ 1 ) (n+ 1 ^2 ) is
- The value of (- 12+ 3i 2 )^ 1000 is
- One root of (1)^ 1/3 is
- A value of n such that ( 3 2+ i2 )^n=1 is
- Let a=e^ i 2 3 . Then the equation whose roots are a+a^ -2 and a^2+a^ -4 is
- The value of 1+ _ k=0 ^ 14 (2k+1) 15 +i (2k+1) 15 is
- If , and are angles such that + + = , and x= +i , y= +i and z= +i , then xyz is equal to
- If (x+iy)= 1+2i 3+4i , then (x^2+y^2)^2 is equal to
- If z^2+z+1=0, where z is a complex number, then the value of (z+ 1z )^2+ (z^2+ 1 z^2 )^2+ (z^3+ 1 z^3 )^2+ + (z^6+ 1 z^6 )^2 is