Complex Numbers and Quadratic Equations
The multiplicative inverse of (−2+5i) is
If ∣2z−1∣=∣z−2∣ and z1,z2,z3 are complex numbers such that ∣z1−α∣<α,∣z2−β∣<β, then ∣α+βz1+z2∣
Write the correct letter from column (2) against column (1):
(a)Re z=0 (i)Re z2=0
(b)Arg z=π/4 (ii)Im z2=0
(iii)Re z2=Im z2.
f(z) when divided by z−i gives remainder i−1; when divided by z+i gives remainder i+1. When f(z) is divided by z2+1, the remainder is