Complex NumbersHard
Question
Number of roots of the equation z10 - z5 - 992 = 0 with real part negative is :
Options
A.3
B.4
C.5
D.6
Solution
z10 - z5 - 992 = 0
z5 = 32
z = 2.
r = 0, 1, 2, 3, 4
for n = 3,4 roots have negative real part.
z5 = - 31
π/5
z =
r = 1, 2, 3 ⇒ roots have negative real part
5 roots have negative real part.
z5 = 32
z = 2.
r = 0, 1, 2, 3, 4
for n = 3,4 roots have negative real part.
z5 = - 31
π/5
z =
r = 1, 2, 3 ⇒ roots have negative real part
5 roots have negative real part.
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
If complex numbers z1, z2, z3 represent the vertices A, B, C of a parallelogram ABCD respectively, then the vertex D is ...The polar form of −5(cos 40o − i sin 40o) is...In G.P. the first term & common ratio are both (√3 + i), then the absolute value of its nth term is :...If roots of xn −1 = 0 are ω1,ω2 , .....,ωn, then- ω1n−1 + ω2n−1 + ...... + &#...If z = (3 + 7i) (p + iq), where p, q ∈ I - {0}, is purely imaginary, then minimum value of |z|2 is...