A little Complex question?

dolina dahani

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Mar 22, 2020
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Hi there, I'm sorry if I made a mistake and put the thread in the wrong place. I have just a little question, I know how to do it but I'm just wondering something. So the question asks to find what Z1/Z2 is and (Z1/Z2)^2012 in algebraic and trigonometric form yet as a result they use exponential and then they transform it in trigonometric form. Am I missing something? There's also an almost the same question with the same answer. I know how to do it in trigonometric and exponential form but I have no clue how to do it in algebraic... The 5th question :)


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\(z_1=-1+i=\sqrt{2}\exp\left(\dfrac{3\pi i}{4}\right)\) and \(z_2=\sqrt3-i=2\exp\left(\dfrac{-\pi i}{6}\right)\)

We use the polar form for large powers for ease of computation
 
If (I don't know your language) they are asking for the result "in algebraic and trigonometric form", that doesn't mean they require you to do the work in a particular form. You do what's easiest, and then give them the form they want. They're teaching you to think that way. (I suppose "algebraic form" means 'a + bi".)
 
If (I don't know your language) they are asking for the result "in algebraic and trigonometric form", that doesn't mean they require you to do the work in a particular form. You do what's easiest, and then give them the form they want. They're teaching you to think that way. (I suppose "algebraic form" means 'a + bi".)
In my experience (western mathematics) there are two forms of a complex number, the rectangular and the polar form.
I suspect that algebraic, \(a+bi\), forms are what we know as the rectangular form.
Also, what we call the polar form is also known as trigonometric form.
I have this standard post:
\( \arg(x + yi) = \left\{ {\begin{array}{{rl}} {\arctan \left( {\frac{y}{x}} \right),}&{x > 0} \\ {\arctan \left( {\frac{y}{x}} \right) + \pi ,}&{x < 0\;\& \;y > 0} \\ {\arctan \left( {\frac{y}{x}} \right) - \pi ,}&{x < 0\;\& \;y < 0} \end{array}} \right. \)
 
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