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

given the complex number z such that z−4i=a+3zi. find the value of a if z is purwly imaginary

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

z−3zi = a + 4i ⇒ z = ((a + 4i)/(1−3i)) ⇒ z = (((a + 4i)(1 + 3i))/((1 + 3i)(1−3i))) = ((a + 3ai + 4i−12)/(10)) ⇒ z = ((a−12)/(10)) + ((3a + 4)/(10))i If z is purely imaginary, then Re(z) = 0 ⇒ ((a−12)/(10)) = 0 ⇔ a = 12

Commented byhardylanes last updated on 01/Jul/20

thanks