Q41 of 66 Page 91

Which of the following is correct for any two complex numbers z1 and z2?

Let z1 = |z1| (cos θ1 + i sin θ1) and z2 = |z2| (cos θ2 + i sin θ2)


Now, z1z2 = |z1| |z2| (cos θ1 + i sin θ1) (cos θ2 + i sin θ2)


= |z1| |z2| [cos θ1 cos θ2 + i sin θ1 cos θ2 + i cos θ1 sin θ2 + i2 sin θ1 sin θ2]


= |z1| |z2| [cos (θ1 + θ2) + i sin (θ1 + θ2)]


⇒ |z1 z2| = |z1| |z2|


And arg (z1 z2) = θ1 + θ2 = arg (z1) + arg (z2)


⇒ |z1 + z2| = |z1| + |z2| is true only when z1, z2 and O are collinear.


Also, |z1 + z2| ≥ ||z1| - |z2||

More from this chapter

All 66 →
39

If , then

 40

A real value of x satisfies the equation if α2 + β2 =

 42

The point represented by the complex number 2 – i is rotated about origin through an angle π/2 in the clockwise direction, the new position of point is:

 43

Let x, y ϵ R, then x + iy is a non real complex number if: