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Expert: Alon Mandes - 12/1/2008


Question
My  problem is to multiply (5 cis 100 degrees) (4 cis 230 degrees). I have to express the answer in rectangular coordinates and give an exact answer.
I do not understand this problem despite examples in my book. Thank you for your help.

Answer
Hello Keli ,
This presentation of complex numbers is called polar. Let's refresh
our memory regarding complex rules :
rcis(Ø)=rcos(Ø)+rsin(Ø) "This is the rectangular presentation".
r*cis(Ø)* ρ*cis(θ)=rρ*cis(Ø+θ). Now, let's get back to the
exercise :
(5 cis 100º ) (4 cis 230º ) = 20 cis 330º. Let's confirm that :
20 cis 330º = 20 cos 330º + i 20 sin 330º =  20*(√3/2)-i 10 .

5 cis 100º = 5 cos 100º + 5 sin 100º = -.868 + 4.924 i
4 cis 230º = 4 cos 230º + 4 sin 230º = -2.571 - 3.064 i
(-.868 + 4.924 i)*(-2.571 - 3.064 i)= 17.318-.10i=20*(√3/2)-i 10 .

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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