Use De Moivres Theorem to compute the following q 3cos27 i

Use De Moivre\'s Theorem to compute the following: (q) [3(cos(27) + i sin (27]^5 (r) ^3 Squareroot 8 (cos (4 pi/5) + i sin (4 pi/5)) Answer:

Solution

10)

(q)

[3(cos(27^o)+isin(27^o))]⁵

=3⁵(cos(27^o)+isin(27^o))⁵

=3⁵(cos((5*27)^o)+isin((5*27)^o))

=3⁵(cos135^o+isin135^o)

=243(-(1_/2)+i(1_/2))

=-(243_/2)+i(243_/2)

=-((2432)_/2)+i((2432)_/2)

=-171.827+ i171.827

-------------------------------------------------------------------

(r)

³[8(cos(4_/5)+isin(4_/5))]

=[8(cos(4_/5)+isin(4_/5))]^1/3

=8^1/3(cos(4_/5)+isin(4_/5))^1/3

=2(cos(4_/3*5)+isin(4_/3*5))

=(2cos(4_/15)+i 2sin(4_/15))

=1.33826 +i1.48629