Power of a Complex Number s 53-68, use DeMoivre\'s Theorem ower of the complex n

Question

Power of a Complex Number s 53-68, use DeMoivre's Theorem ower of the complex number. 6.6 Trig . 95.O to rite the result in standard for . Oh Ohm m. os 20 + i sin + i sin n 209)13 54. [3(cos 60° + i sin 60) alter . circ 0° + i sin 53. I5lcos cos 4 rising)12 56.12(ng + isin)] whe 4 in in 3.2)1 58. (cos 0+ i sin 0)20 e cu an 1T 57. [5(cos 3.2 os 15 + i sin 15°)]460 59 B(cos 61 + i)s 63 1 t6 65. 23 + i)10 cos 62. (2 2i)6 64. (3 28 66. 4(1 - ./??)" 68. 4 67 (3 Graphing Powers In and 70, represent the powers z, z2, z3, and Exercises 69 graphically. Describe the pattern.

Explanation / Answer

[ 3 ( cos 15 + i sin 15 ) ]^4

= [ 3^4 ( cos 4*15 + i sin 4*15 )]

= 81 ( cos 60 + i sin 60 )

= 81 ( 1/2 + sqrt 3/2 i )

= 81/2 +81i sqrt 3 / 2

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