Complex Numbers questions
967 published questions with worked solutions.
- If z= ( 3 2 + i 2 )^ 107 + ( 3 2 - i 2 )^ 107 , then what is the imaginary part of z equal to?
- What is the number of distinct solutions of the equation z^2+|z|=0 (where z is a complex number)?
- What is 1+ ^2 1+ equal to, where is the cube root of unity?
- The value of i^ 2n +i^ 2n+1 +i^ 2n+2 +i^ 2n+3 , where i= -1 , is
- The value of ( -1+i 3 2 )^n+ ( -1-i 3 2 )^n where n is not a multiple of 3 and i= -1 , is
- If 1, , ^2 are the cube roots of unity, then (1+ )(1+ ^2)(1+ ^3)(1+ + ^2) is equal to
- The modulus and principal argument of the complex number 1+2i 1-(1-i)^2 are respectively
- If |z+4| 3, then the maximum value of |z+1| is
- The number of roots of the equation z^2=2 z is
- The smallest positive integer n for which ( 1+i 1-i )^n=1, is
- If |z- 4 z |=2, then the maximum value of |z| is equal to
- Geometrically Re (z^2-i)=2, where i= -1 and Re is the real part, represents
- What is the principal argument of (-1-i), where i= -1 ?
- The number of non-zero integral solutions of the equation |1-2i|^x=5^x is
- If and are different complex numbers with | |=1, then what is | - 1- | equal to?
- What is i^ 1000 +i^ 1001 +i^ 1002 +i^ 1003 equal to (where i= -1 )?
- The modulus-amplitude form of 3 +i, where i= -1 is
- What is the value of the sum _ n=2 ^ 11 (i^n+i^ n+1 ), where i= -1 ?
- What is the value of ( -1+i 3 2 )^ 3n + ( -1-i 3 2 )^ 3n , where i= -1 ?
- Which one of the following is correct in respect of the cube roots of unity?
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