How can you simplify complex division with imaginary numbers?

[alijan kk]

Homework Statement

(1+2i+3i²)/(1-2i+3i²)

answer options : a : 1 b: -i c: i d: 0

Homework Equations

what is the most easy method to solve it ,

The Attempt at a Solution

are they conjugate to each other ? if they are than z/zconjugate =1 ,
but how can i make shure that they are conjugate to each other
[/B]

 

[Mark44]

Homework Statement

(1+2i+3i²)/(1-2i+3i²)

answer options : a : 1 b: -i c: i d: 0

Homework Equations

what is the most easy method to solve it ,

Simplify the $i^2$ term in the numerator and denominator, and then multiply both numerator and denominator by the conjugate of the denominator. You should already know that $i^2 = -1$.

The Attempt at a Solution

are they conjugate to each other ? if they are than z/zconjugate =1 , [/B]

That's not true. $\frac z {\bar z} \neq 1$ unless z is purely real.

but how can i make shure that they are conjugate to each other

 

[andrewkirk]

Step 1, convert each of the numerator and denominator into the form $a+bi$ by replacing $i^2$ by a number that doesn't involve $i$ in both, then collecting terms and simplifying.
Step 2: Make the denominator real by multiplying both the numerator and the denominator by the conjugate of the denominator.
Step 3: simplify.

 

[alijan kk]

Simplify the $i^2$ term in the numerator and denominator, and then multiply both numerator and denominator by the conjugate of the denominator. You should already know that $i^2 = -1$.
That's not true. $\frac z {\bar z} \neq 1$ unless z is purely real.

i simplified the equation and i got (1-i)/(1+i) and by dividing it I got -i. which is the correct answer in the book , thankyou.