Answer:
1) 9/cos(θ)
2)4[tex]\sqrt{3}[/tex](cos(198) +isin(198))
3)z= cos(π/3) +isin(π/3)
Step-by-step explanation:
x=9
i.e. x= 9 +i0
θ= tan^-1 (0/9)
θ= tan^-1 (0)
=0
hence z= r(cosθ +i sinθ)
= 9(cos 0 + isin 0)
= 9
As cos (0) = 1 hence polar form of x=9 is 9/cos(θ) where θ=0
2)
Given
z1=2[tex]\sqrt{3}[/tex]( cos(116)+isin(116))
z2=2(cos(82)+isin(82))
As per the product formula od complex polar numbers:
z1.z2= r1.r2(cos(θ1+θ2) +isin(θ1+θ2) )
Putting the values
= 4[tex]\sqrt{3}[/tex](cos(198) +isin(198))
3)
z= 1/2 + i[tex]\sqrt{3}[/tex]/2
r= [tex]\sqrt{(1/2)^{2}+(\sqrt{3}/2) ^{2} }[/tex]
r = [tex]\sqrt{1/4 +3/4} \\\sqrt{4/4}\\\sqrt{1}[/tex]
r=1
θ= tan^-1 [tex](\sqrt{3}/2 ) / (1/2)[/tex]
= tan^-1[tex]\sqrt{3}[/tex]
=60
=π/3
hence
z= cos(π/3) +isin(π/3) !
