Complex Number and Quadratic Equations
Let αand βbe the roots of equation x2−6x−2=0. If an=αn−βn,forn≥1, then the value of 2a9a10−2a8is equal to:
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Consider the complex numbers z=(1+i cos θ)(1−i sin θ),The value of θ for which z is purely imaginary real are,
[2−z1z2z1−2z2]=1 and ∣z2∣=1 then the value of ∣z1∣ 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.
The multiplicative inverse of 3−4i
Consider the following statements: S1:−8=2i×4i=(−4)×(−16)S2:(−4)×(−16)=(−4)×(−16)S3:(−4)×(−16)=6464=8Of three statements, the incorrect one is:
If z1,z2,z3 are complex numbers such that z1a+z2b+z3c=1+i & az1+bz2+cz3=0, then the value of z12a2+z22b2+z32c2 is