Question

I NEED HELP PLEASE AND THANK YOU!!!!

Answer 1

1) 9/cos(θ)

2)4
`√(3)`(cos(198) +isin(198))

3)z= cos(π/3) +isin(π/3)

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
`√(3)`( 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
`√(3)`(cos(198) +isin(198))

3)

z= 1/2 + i
`√(3)`/2

r=
`\sqrt{(1/2)^(2)+(√(3)/2) ^(2)  }`

r =
`√(1/4 +3/4) \\√(4/4)\\√(1)`

r=1

θ= tan^-1
`(√(3)/2 ) / (1/2)`

= tan^-1
`√(3)`

=60

=π/3

hence

z= cos(π/3) +isin(π/3) !