Complex Number and Quadratic Equations
If α,β∈C are distinct roots of the equation x2−x+1=0 then α101+β107 is equal to
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If the six solutions of x6=−64 are written in the form a+bi, where a and b are real, then the product those solution with a<0, is
If ∣z1∣=1,∣z2∣=2,∣z3∣=3 and ∣9z1z2+4z1z3+z2z3∣=12, then find the value of ∣z1+z2+z3∣.
If ∣z−3+2i∣≤4 then the difference between the greatest value and the least value of ∣z∣ is:
If the expression [1+2i sin(2x)][sin(2x)+cos(2x)+itan(x)] is real, then the set of all possible values of x is
If z is a complex number of constant modulus such that z2 is purely imaginary then the number of possible values of z is?
Assertion :If z1+z2=a and z1z2=b where a=a and b=b, then arg(z1z2)=0. Reason :The sum and product of two complex numbers are real if and only if they are conjugate of each other.
If z=23−i, then (i101+z101)103 equals