the complex number Z satisfies

Question

(Z+i)/(1+2i)= iz

Find Z.

please help thx!

Answer 1

Multiply it out.
z + i = zi -2z
3z = i(z-1)
(z-1)/z = 3/i = -3i
1 - (1/z) = -3i
1/z = -3i - 1
z = -1/(3i + 1)
Now multiply numerator and denominator by (3i -1)to make the denominator real.
z = -(3i -1)/(-9 -1)
= (3/10)i - (1/10)
Check my thinking and accuracy. My algebra tends to be sloppy.

Answer 2

Thank you so much!!!