1.

`z_(1) and z_(2)` are the roots of the equaiton `z^(2) -az + b=0` where `|z_(1)|=|z_(2)|=1` and a,b are nonzero complex numbers, thenA. `|a| le 1`B. `|a| le 2`C. `arg(a^(2)) = arg(b)`D. `agr a = arg(b^(2))`

Answer» Correct Answer - B::C
`z_(1)` and `z_(2)` are the roots of the equation `z^(2) -az + b=0`. Hence, `z_(1)+z_(2) = a,z_(1)z_(2) = b`
Now `,|z_(1) +z_(2)| le |z_(1)| + |z_(2) |`
` rArr |z_(1) + z_(2)| = |a| le |1+1=2" "(because |z_(1)|=|z_(2)| =1)`
`rArr arg(a) = (1)/(2)[arg(z_(2) + arg(z_(1))]`
Also , arg(b) `= arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2))`
`rArr 2 arg (a) = arg (b)`


Discussion

No Comment Found

Related InterviewSolutions