# Review of Complex Algebra

- StudyBlue
- Australia
- University of Technology, Sydney
- Mathematics
- Mathematics 33360
- Various
- Review of Complex Algebra

**Created:**2012-06-07

**Last Modified:**2014-08-10

#### Related Textbooks:

Advanced Engineering Mathematics, Third Edition#### Related Textbooks:

Multivariable Calculus: Concepts and Contexts (Stewart's Calculus Series)^{2}- d

^{2})

+ (bc - ad) / (c

^{2}- d

^{2})i

ιzι = √(x

^{2}+ y

^{2})

r is the modulus ιzι

θ is the angle between Re axis & r

θ = arctan y/x

^{x}has the property such that f(x + y) = ?

^{iθ}= cosθ + isinθ

θ = arctan(2√3)/2 = π/3

z = 4( cos(π/3) + isin(π/3))

θ = -π/2

z = 3(cos(π/2) - isin(π/2))

θ = arctan √2/√6 = -5π/6

z = 2√2 (cos(-5π/6) + isin(-5π/6))

Exponential: z = 2√2e

^{-i5π/6}

_{1}= r

_{1}(cosθ

_{1}+ isinθ

_{1})

z

_{2}= r

_{2}(cosθ

_{2}+ isinθ

_{2})

z

_{1}z

_{2 = ?}

_{1}r

_{2 }(cos(θ

_{1}+θ

_{2})) + isin(θ

_{1}+θ

_{2}))

_{1}= r

_{1}(cosθ

_{1}+ isinθ

_{1})

z

_{2}= r

_{2}(cosθ

_{2}+ isinθ

_{2})

z

_{1 / }z

_{2}= ?

_{}

_{1}/r

_{2}) (cos(θ

_{1}-θ2) + isin(θ

_{1}-θ

_{2})

_{})

z

^{n}= r

^{n}e

^{inθ}

z

^{n}= (r(...?))

^{n}

= r

^{n}(...)

^{n}= (r(cos θ + isin θ))

^{n}

z

^{n}= r

^{n}(cos nθ + isin nθ)

^{n}= r

^{n}e

^{inθ}

_{0}= 3(cos70 + isin70)

w

_{1 }= 3(cos90 + isin90)

w

_{2}= 3(cos310 + isin310)

Solution shown at www.youtube.com/watch?v=xPn8pHCZL18

_{0}= 3(cos0 + isin0)

w

_{1}= 3(cos2π/3 + isin2π/3)

w

_{2}= 3(cos4π/3 + isin4π/3)

#### Words From Our Students

"StudyBlue is great for studying. I love the study guides, flashcards, and quizzes. So extremely helpful for all of my classes!"

Alice, Arizona State University

"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim, University of Florida

"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly! I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer, Rutgers University

"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin, LSU