# Sorry I messed up in my previous question.  let z1= 2 ( cos(pi/5) )+ i sin (pi/5) ) and z2= 8 (cos (7pi/6) + i sin (7pi/6) ) find (z_2)'I have to find z2 and it has a dash on the top. I rewrote...

Sorry I messed up in my previous question.

let z1= 2 ( cos(pi/5) )+ i sin (pi/5) ) and z2= 8 (cos (7pi/6) + i sin (7pi/6) ) find (z_2)'

I have to find z2 and it has a dash on the top.

I rewrote this question because I noticed that I didnt wrote it correctly the first time . thank you!

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The problem requests for you to find `bar(z_2)` , hence, you need to find the conjugate of the complex number `z_2` .

Since the problem provides the polear form of the number, you need to find the rectangular form, such that:

`z_2 = x + i*y`

`cos (7pi/6) = x/8 => cos (6pi/6 + pi/6) = x/8`

`cospi*cos(pi/6) - sinpi*sin(pi/6) = x/8`

Since `cos pi = -1` and `sin pi = 0` yields:

`-cos(pi/6) = x/8 => -sqrt3/2 = x/8 => x = -4sqrt3`

`sin (7pi/6) = y/8 => sin (6pi/6 + pi/6) = y/8`

`-sin (pi/6) = y/8 => -1/2 = y/8 => y = -4`

Substituting `-4sqrt3` for x and -4 for y yields:

`z_2 = -4sqrt3 - 4*i`

You need to find the conjugate of `z_2` , such that:

`bar(z_2) = -4sqrt + 4*i`

Hence, evaluating the conjugate `bar(z_2)` yields `bar(z_2) = -4sqrt + 4*i.`