Question

I will medal and fan! Really, quick, easy question! If z2=8(cos(7pi/6)+isin(7pi/6)), then what is the conjugate of z2?

Answer 1

@agent0smith Could you help me with this one?

Answer 2

The questions asks for the answer to be kept in polar form.

Answer 3

Or @zepdrix Could you help me? Either way would be awesome!

Answer 4

Conjugate is super easy. Change the sign on the imaginary component.

Answer 5

Oh! haha. Easy. Thanks! @agent0smith

Answer 6

Oh yeah i guess you need to change the angle too though...

Answer 7

Why?

Answer 8

Correct polar form means they're both positive.

What you can do is make the i component negative and use the fact that sin(-x) = -sinx:
-isin(7pi/6) = isin(-7pi/6)

So your new angle has to be -7pi/6. You can make it positive by adding 2pi.

Answer 9

Don't forget to also change the angle in the cosine (remember both need to have the same angle)

z2=8(cos( )+isin( )

Answer 10

Haha sorry, I didn't mean that.

Answer 11

570?

Answer 12

or 19pi/6?

Answer 13

-7pi/6 + 2pi = ?

Answer 14

Oh dear. aha dumb brunette moment. 5pi/6 lol

Answer 15

lol yep :)

Answer 16

Great thanks! So it would be 8(cos(5pi/6+isin(5pi/6)?

Answer 17

Yep

Answer 18

I've never needed to find the conjugate of a polar form complex number, so that was new.

Answer 19

Lol, same here. It's pretty dumb that I had to do that, but thanks for helping!

Answer 20

I'm not even sure when you'd need it. Conjugate of a+bi is useful for rationalizing fractions, but... that's not even used in dividing complex numbers.