Please determine all the sixth squareroots of 64 Give your a

Please determine all the sixth squareroots of -64. Give your answer in rectangular form Please express - 12i in polar form. Please express 4cis (5 pi/4) in rectangular form. Please determine the principal value of (1 + i)^3 - 2i. You may leave your answer in polar form. Please evaluate (10 + i) (8 - 2i) Please evaluate (3 + 2i) -(4 - 7i) Please evaluate i^217.

Solution

Solution:

-64=(-1)(64)=(-1) 2⁶

take the sixth root

(-64) ^1/6=(-1)^1/6 ( 2^6)1/6

  =(-1)^1/6 2

r=2 =30 degrees

Rectangular form is z=r(cos +isin )

=2(cos30+isin30)

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

=sqrt(3)+i

(14)

z=0-12i

|z|=12

=-90 Deg

(15)

4cis (5pi/4)=4[cos 5pi/4 +isin 5pi/4]

=4[cos 5*180/4+isin5*180/4]

=4[cos225+isin225]

(17)(10+i)(8-2i)=80-20i+8i-2i²

^{i^2}=-1

(10+i)(8-2i)=80-12i-2(-1)

=80-12i+2

=82-12i

(18)

(3+2i)-(4-7i)=3+2i-4+7i

=-1+9i