SOLUTION: Let z=a+bi. Discuss the values of a and b so that the following will be true: z(i) is a positive real number and z(3-i) is a pure imaginary number.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Let z=a+bi. Discuss the values of a and b so that the following will be true: z(i) is a positive real number and z(3-i) is a pure imaginary number.      Log On


   

Question 1115020: Let z=a+bi. Discuss the values of a and b so that the following will be true:
z(i) is a positive real number and z(3-i) is a pure imaginary number.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
z%2Ai=%28a%2Bbi%29%2Ai
z%2Ai=a%2Aii%2Bb%2Ai%5E2
z%2Ai=-b%2Bai
For this to be real and positive,
b%3C0
.
.
.
z%2A%283-i%29=%28a%2Bbi%29%2A%283-ii%29
z%2A%283-i%29=3a-ai%2B3bi-bi%5E2
z%2A%283-i%29=%283a%2Bb%29%2B%283b-a%29i
For this to be imaginary,
3a%2Bb=0
and
3b-a%3C%3E0