Question

Question 5 Write the complex number in rectangular form. -3(cos 225° +i sin 225°) Question 6 Write the complex number in polar form. Express the argument in degrees. 3cos Oº+isin 0°) 3[cos 180°+ i sin 1809) 3[cos 90° + i sin 90°) O 3(cos 270° Fisin 270°F

Answer 1

1 . I > © -3( cos 225°+ i sin 225°) Ans: First we consider the trigonometry inside in bracket, So, 225° is an angle in the zod quadrant where both sin and cos ratios are negative. I l I 208225º= - 608 (2259-180") (90 to 180) (0 to 90°) sin tue I all tve =-co845° x'- I IT (180*270) (270'to 360) ton tue I cos tve cot tue Y rective i sin 225º = -sin (225-180)" = - sin 45" (osin 45" 268245" cosectue - 4 - 2 ) Now, - 3(608225 tisin 225") =- 3 +33 +3v2 i Ane (in rectangular form) options (52 x 82 =2)

© -3 » Cu, y) = (1, 0) rectangular Polar coordinate coordinate Now, utêy= neoso tisin o) (impolas form) U = r cos o y=reino u r= u2+ y² Here, 1-3,80 (-3, 10) = r(1080, sino) 8080=-3 e ssino = 0 a = √(-372 4072 = 5a = 3 8=3 0080=-3 11 rsino =0 36030 = -3 3sino =0 680 = un sino =0 = sin (180°-0°) 2. coso = -1 = sin 180° = cos(180 - 0°) = 608180° Now, in polar form. -3 or (-3+20) = 3 (693 180° + è 8 in 180º) Am O is satisfying between or equal to <O<T, Tire: 180° Hence, required argument is 180°. (in degrees)