Answer:
a)zw = 44.295 cos(1.924) +isin(1.924))
b) z/w= 4.921 cos(-0.936) + isin(-0.936)
Step-by-step explanation:
Given:
z=13+7i
w=3(cos(1.43)+isin(1.43)
a. convert zw using De Moivre's theorem
First coverting z into polar form:
13^2 + 7^2 = 14.765
[tex]\sqrt{14.765}[/tex] =r
θ= arctan (7/13)
= 0.49394 (28.301 in degrees)
z= 14.765(cos(0.49394)+isin(0.49394) )
Now finding zw
zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))
Using De Moivre's theorem, the modulus will be multiplied
14.765 x 3=44.295
whereas the angles will be added
.494+1.43=1.924
Thus:
zw = 44.295 cos(1.924) +isin(1.924))
b)
finding z/w
z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))
Using De Moivre's theorem, the modulus will be divided
14.765 / 3 = 4.921
whereas the angles will be subtracted:
.494-1.43=-0.936
Thus:
z/w= 4.921 cos(-0.936) + isin(-0.936) !
