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,
If z is a complex number satisfying z4+z3+z2+z+1=0, then ∣z∣ is equal to ____.
Prove that:(1−i)n(1−i1)n=2n for all values of n∈N.
Show that (1+i)n(1−i1)n=2n for all n∈N.
If n is a positive integer than show that(1+i)2n+(1−i)2n=2(n+1)cos(nπ/2)
If z is a complex number, then ∣3z1∣ = 3 ∣z2∣ represents
Given that the real parts of 5+12i and 5−12i are negative. Then the numberz=5+12i−5−12i 5+12i+5−12i reduces to
Find the multiplicative inverse of the complex numbers given the following:4−3i