Hi guys, just before i ask this question i would like to let you know that i am a year 11 student, who has decided to study next years Specialist math (highest level of maths) course early to get a head start as i am nervous for next year(year 12.) :)(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

and

The first one i understand part A and B i have attempted C but am not sure if it the correct method and D i have attempted but have not found an answer, i believe they are related to the second picture. I do not understand how that formula works and need help understanding it, what is the purpose of it?

2. Relevant equations

and cisӨ=CosӨ+isinӨ

3. The attempt at a solution

z =2cisӨ

A) |z| = 2

arg z = Ө

B)

_

Z = 2(cosӨ-isinӨ)

= 2cosӨ-isinӨ

= 2cos(-Ө)+isin(-Ө)

= 2cis(-Ө)

C) -z = -2cisӨ

= -2(cosӨ+isinӨ)

= -2cosӨ-isinӨ

= -2cosӨ+isin(-Ө)

From here i am stuck, the textbook shows the answer as 2cis(Ө+∏)

D)

_

-Z = -2(cosӨ-isinӨ)

= -2cosӨ+2isin(-Ө)

From here i am stuck again, the textbook shows the answer as 2cis( ∏-Ө)

I believe the answers are used using the formula stated above cis(Ө+k2∏)=cisӨ but i do not understand what it means or why it is used

Please remember that i am self-teaching myself this subject at the moment and will be undertaking it next year for year 12.

Thanks!! :)

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# Homework Help: Complex number theorem help

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