# SOLUTION: Hi there... i just have a few questions that i would like to ask regarding complex numbers. 1){{{1-sqrt(3)*i}}} i would show you how much i can do on this one... however, im co

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi there... i just have a few questions that i would like to ask regarding complex numbers. 1){{{1-sqrt(3)*i}}} i would show you how much i can do on this one... however, im co      Log On

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 Algebra: Complex Numbers Solvers Lessons Answers archive Quiz In Depth

 Question 207423: Hi there... i just have a few questions that i would like to ask regarding complex numbers. 1) i would show you how much i can do on this one... however, im completely stuck sorry and i was unable to find a proper square root sign, so hope that its alright. 2) I REALLY strggle with De Moivre's theorem. for this question i have to find the following: a) b)find when c)write in polar form d}find or using De Moivre's theorem. SO those are all my questions, hope they are alright Thanks Christelle :DAnswer by Edwin McCravy(8879)   (Show Source): You can put this solution on YOUR website!``` I'll just do (2) and you can use it as a model to do (1). Let's draw the picture of that complex number as a right triangle on a graph. where , ``` (a) . ``` Sometimes this is called the "modulus". This is the length of the hypotenuse of that right triangle. We find it the same way we always find the hypotenuse, the Pythagorean theorem: We label the hypotenuse and this is the same as ``` (b) find when ``` "Argument" means "angle" (you can remember it because "argument" and "angle" both start with "a" and their third letters are "g") Now since we are told that the argument is between and , we must take the argument as a negative angle measured by rotating clockwise from the right side of the x-axis, indicated by the blue arc below labeled , "phi". It should be q, "theta", but I can't get that Greek letter on the notation program for this site, so I'll use instead. Since the triangle is an isosceles right triangle, its interior angles are or in radians. However since tells us that the rotation is clockwise from the right side of the x-axis, the angle is taken as negative. Thus we take it as and we label it: ``` (c) write in polar form: ``` Since , therefore and since , therefore So and we can factor out and get: This is the polar form of Therefore since and ``` (d) or (sqrt(2)-i*sqrt(2))^6}}} ``` DeMoivre's theorem says: Therefore: Since is coterminal with , we have Edwin```