pu4l6-converting-between-polar-and-rect-forms-of-complex-numbers-precalculus

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In this tutorial, we go over how to covert complex numbers from rectangular to polar form and the reverse. We show you the strategy steps and algorithm to accomplish the conversion process. The process of converting complex numbers from rectangular to polar form involves first knowing what the two forms are. The rectangular form of complex numbers is x+yi or a+bi and the polar form of complex numbers can be written as r(cos theta + i sin theta) r ( cos θ + i sin θ) you first find r using the pythagorean theorem. the formula r = sqrt ( x^2 + y^2) will help you find the value of r. r is known as the radius. And the angle theta θ is the angle from zero degrees to the graph of the complex number. To find the angle theta θ you use the formula θ=tan ^-1 (y/x) arctan of y divided by x will give you the reference angle. You then have to graph the coordinates and use ASTC to determine the terminal side and find the value of theta θ. The process for going from polar to rectangular is quite different. To accomplish this you have to determine r and theta from the polar form then use x=r cos θ and y=r sin θ to find the real and imaginary parts of the complex number in polar form. The unit circle is also helpful in finding the inverse sine and also evaluating the angles at common angular values. If the angles are not common then the use of a calculator will be necessary in evaluating the sine and cosine functions also the inverse tangent function

Tagged under: law sines,law cosines,vectors,plane,dot,complex numbers,magnitude,direction,geometrically,operations,oblique,AAS,ASA,SSA,ambiguous,component,real,demoivre,+bi,imaginary axis,rcos θ,isin θ,argument,modulus,polar,restricted,quadrant,multiplication,division,powers,root,nth root,theorem θ + sin θ,scalar,cross product,larson,examples,steps, ,python,applications,basics,book,notes,cheat sheet,desmos,equations,arctan

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