Complex Numbers questions
967 published questions with worked solutions.
- If a > 0 and z= (1+i)^2 a+i , (i= -1 ) has magnitude 2 5 , then z is equal to
- If x= -1- -1- -1- -1- , where is a non-real complex cube root of unity, then the value of x is..
- The polar form of the complex number z= 1 1+i , (where i= -1 ) is
- If (3x + 2) – (5y-3)i and (6x + 3) + (2y – 4)i conjugates of each other, then the value of x-y x+y is (where i = -1 , x,y )
- The value of i^ 248 +i^ 246 +i^ 244 +i^ 242 +i^ 240 i^ 249 +i^ 247 +i^ 245 +i^ 243 +i^ 241 , (i= -1 ) is
- If a>0 and z= (1+i)^2 a-i , i= -1 , has magnitude 2 5 , then z is
- If is a complex cube root of unity, then the value of [ ( ^ 10 + ^ 23 )- 4 ]=
- If is a complex cube root of unity, then the value of the expression 2 (1+ 1 ) (1+ 1 ^2 )+3 (2+ 1 ) (2+ 1 ^2 )+ +(n+1) (n+ 1 )...
- If n is a positive integer, then (1 + i 3 )^ 2n + (1 - i 3 )^ 2n is equal to....
- If z_1 = 5 - 2i and z_2 = 3 + i, where i = -1 then ( z_1 + z_2 z_1 - z_2 ) is
- ( 2 + i 2 )^7 ( 4 + i 4 )^3 =
- If and are the distinct roots of the equation x^2 - x + 1 = 0, then the value of ^ 200 + ^ 206 + 2 is equal to
- The value of ( -1+i 3 2 )^ 18 + ( -1-i 3 2 )^ 18 is
- The modulus of the square root of the conjugate of -7+24 -1 is ...
- If z= _ n=0 ^ 2026 i^ n , where i= -1 , then one of the values of z is ...
- The smallest positive integer n for which (1+i)^n (1-i)^ n-2 is a real number, is ...
- The value of ( +i )^4 ( +i )^5 = where i= -1
- The equation |z + 1 - i| = |z - 1 + i| represents a (where z is a complex number)
- If i = -1 then [ i^ 18 + ( 1 i )^ 25 ]^3 =
- If w is a complex cube root of unity, then the value of w^ 10 -w^7+w^5-w^2+1 is
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