express in terms of z (1+2i)z = 5

Question

everyone else got the answer z = (1-2i) but i cant get to this

Answer 1

(1 + 2i)z = 5

 

Multiply both sides of the equation by (1 - 2i) ,

This will give,        

(1 + 2i)(1 - 2i)z = 5(1 - 2i)

(1 - 2i + 2i - 4i²)z = 5 - 10i

 

Now since,  i² = -1

This becomes,

(1 - 4(- 1))z = 5 - 10i

(1 + 4)z = 5 - 10i

5z = 5 - 10i

 

Now divide both sides of the equation by 5,

z = 1 - 2i                 ,

which is the answer you wanted to find. If you don't understand why or how I did this then please feel free to ask .