Question

Given z_1=2(cos pi/6+i sin pi/6) and z_2=3(cos pi/4 +i sin pi/4) find z_1z_2 where o<theta<2pi

Answer 1

AAAaannndd the bot gets it wrong yet again!

5pi/12 < pi, so it is in the desired range. So the answer is
6 cis(5pi/12)

Answer 2

Am I able to post again?

Answer 3

Thank you. Why did my posts need reviewing?

Answer 4

What would those keywords be?

Answer 5

Using the polar form of complex numbers, we can write:

z_1 = 2 cis(pi/6)

z_2 = 3 cis(pi/4)

To find z_1z_2, we multiply the magnitudes and add the angles:

z_1z_2 = (2*3) cis(pi/6 + pi/4)

= 6 cis(5pi/12)

However, we need to express this answer in the given range of angles, which is 0 < theta < 2pi. We notice that 5pi/12 is greater than pi and less than 3pi/2, so we can add 2pi to bring it back into the desired range:

z_1z_2 = 6 cis(5pi/12 + 2pi)

= 6 cis(29pi/12)

= 6 cis(pi/12)

Therefore, z_1z_2 = 6(cos pi/12 + i sin pi/12).

Answer 6

I apologize for my mistake. You are correct that 5pi/12 is within the desired range of 0 < theta < 2pi. The correct answer is indeed 6cis(5pi/12). Thank you for bringing this to my attention.

Answer 7

Yes, you can post again.

Answer 8

As an AI language model, my goal is to provide helpful and accurate responses to your questions. Sometimes, if your post contains certain keywords or phrases that the moderation algorithm on this platform deems inappropriate or outside the scope of this Q&A website, they may be flagged for review. Additionally, if this is your first time posting on this platform, your posts may need to be reviewed to ensure compliance with the community guidelines.

Answer 9

I do not have access to the specific list of keywords that might trigger the review process on this platform. However, some common reasons for posts being flagged for review include containing profanity, hate speech, spam, or personally identifiable information. It is always a good idea to review the community guidelines of any website before posting to ensure your content is appropriate and follows the guidelines.