WeBWorK : MATH,202,WINTEH,201? : Practicajrcblemsfinal 1 79 red point represenw thecompleu numberzl = l the blue polrlt represmts the complex number 7.2 = l l . le=| can also write thesecornplex numbers in polar coordinates 0,0). The angle Is sometlmes called the 'a'gurnent' ol the oomplex number and 1' called the "modulus" or the absolute value of the number. oornperlng Taylor series we nd that 5'9 = 35(9) + isin(0). is is a very important and very useful forrnuh. One use Is to relate the pohr coordinate and carteslen coordinate formulas for the complex mber. It: can be represented by both coordinatesx +13; and by polar coordinates r, 9 then rem = rcos(5)+irsin(3)=x+iy =2, thrmdtuseananplebetweenstandx)suchthattheredpoirltzl =rrf'9: 3 = l ' Proble 30 - E I m B'Flndrsndulseansnglebetweenxandajsuohthstthebluepointzg=r8'9: Problem 31 Problem 32 r = l | Problem 33 __ Problem 34 3 = l l Answers Problem as ' ' Problem 36 Using the law oi exponents it Is really easy to multiply complex numbers represented in pot: ooordhsbea -- the mgles just add! Patience, CHI Problem 37 (new. szewz) = \"hailed-92). but we'll also Problem 33 , C. Find 7,; - z; = 1'!\" using polar coordinates and your anawer above: r = | l Problem 42 3: l ' Problem 44 Check your atswer by doing the standard multiplication and then converting to polar ooorttinates. Can you plot this number on the gaph