Question

If z = − vector z, then :

(a) z is purely real
(b) z is purely imaginary
(c) z is any complex number
(d) real part of z = complex

Answer 1

When z = -z for a complex number z, it implies z must be purely imaginary, as the real part would have to be zero for z to be equal to its own negative.

Step-by-step explanation:

If z = - vector z, this means that every component of z is multiplied by -1. For a complex number, z, to satisfy this condition, it should be equal to its negative. This would only be possible if z is zero or purely imaginary. If z is expressed as a + bi (where a and b are real numbers), the only way for the equality z = -z to hold is if a = 0 and b is any real number, meaning z is 0i + bi, which is purely imaginary. Therefore, the answer to the question is (b) z is purely imaginary.