Complex Number and Quadratic Equations
A complex number z is said to be unimodular if . Suppose z1and z2are complex numbers such that 2−z1z2z1−2z2is unimodular and z2is not unimodular. Then the point z1lies on a :
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Prove that:(1−i)n(1−i1)n=2n for all values of n∈N.
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 z is a non-zero complex number, then ∣∣zzˉ∣zˉ∣2ˉ∣∣ is equal to
The smallest positive integer n for which (1−i)(1+i)n=1 is
Find the multiplicative inverse of the complex numbers given the following:−i
tani[loge(a+iba−ib)] is equal to
If z1z2∈C,z12+z22ϵR,z1(z12−3z22)=2 and z2(3z12−z22)=11, then the value of z12+z22 is
If z1,z2,z3 are three points lying on the circle ∣z∣=2 then the minimum value of ∣z1+z2∣ 2+∣z2+z3∣ 2+∣z3+z1∣ 2 is equal to