given-the-complex-number-z-such-that-z-4i-a-3zi-find-the-value-of-a-if-z-is-purwly-imaginary-

Question Number 101159 by hardylanes last updated on 30/Jun/20

g i v e n t h e c o m p l e x n u m b e r z s u c h t h a t

z - 4 i = a + 3 z i .

f i n d t h e v a l u e o f a i f z i s p u r w l y i m a g i n a r y

Answered by Rio Michael last updated on 01/Jul/20

z - 3 z i = a + 4 i

\Rightarrow z = \frac{a + 4 i}{1 - 3 i}

\Rightarrow z = \frac{(a + 4 i) (1 + 3 i)}{(1 + 3 i) (1 - 3 i)} = \frac{a + 3 a i + 4 i - 12}{10}

\Rightarrow z = \frac{a - 12}{10} + \frac{3 a + 4}{10} i

If z is purely imaginary, then R e (z) = 0

\Rightarrow \frac{a - 12}{10} = 0 \Leftrightarrow a = 12

Commented by hardylanes last updated on 01/Jul/20

thanks