Complex Number and Quadratic Equations
Let a,b,xandy be real numbers such that a−b=1andy=0. If the complex number z=x+iy satisfies Im(z+1az+b)=y , then which of the following is (are) possible value9s) of x? (a)−1−1−y2 (b) 1+1+y2(c)−1+1−y2 (d) −1−1+y2
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If z1,z2,z3 are 3 distinct complex numbers such that ∣z2−z3∣3=∣z3−z1∣4=∣z1−z2∣5, then the value of z2−z39+z3−z116+z1−z225 equals
If ∣z1∣=∣z2∣ and arg (z1/z2)=π, then z1+z2 is equal to
Find the multiplicative inverse of the complex numbers given.5+3i.
Which of the following statement is correct ?
The value of (1+i1−i)10+(1−i1+i)8=
If z1,z2,z3,z4 are complex numbers in an Argand plane satisfying z1+z3=z2+z4. A complex number ′z′ lies on the line joining z1 and z4 such that Arg(z1−z2z−z2)=Arg(z−z2z3−z2). It is given that ∣z−z4∣=5,∣z−z2∣=∣z−z3∣=6 then
Number of complex numbers z satisfying Z3=Z_ is