Complex NumbersHard

Question

If |z1| = 2, |z2| = 3, |z3| = 4 and |2z1 + 3z2 + 4z3| = 4, then absolute value of 8z2z3 + 27z3z1 + 64z1z2 equals

Options

A.24
B.48
C.72
D.96

Solution

8 z2 z3 + 27z3 z1 + 64 z1 z2 = 2. z1 z2 z3 + 3. z2 z3 z1 + 4z1 z2 z3
(∵ 4 = z1, 9 = z2, 16 = z3)
= (2 + 3 + 4) (z1 z2 z3) = (z1 z2 z3)
So absolute value = 4.  2. 3. 4 = 96

Create a free account to view solution

View Solution Free
Topic: Complex Numbers·Practice all Complex Numbers questions

More Complex Numbers Questions

If z = x + iy and |z − 3| = R(z), then locus of z is-...If z = x + iy and z1/3 = a - ib then = k(a2 - b2) where k =...=...If g(x) and h(x) are two polynomials such that the polynomial P(x) = g(x3) + xh(x3) is divisible by x2 + x + 1, then -...If |z| = max {|z - 1|, |z + 1|}, then...