Write the complex number in the form a + bi.
3(cos 60° + i sin 60°)

The complex number in the form of a + b i is 3/2 + i √3/2

Step-by-step explanation:

* Lets revise the complex number in Cartesian form and polar form

- The complex number in the Cartesian form is a + bi

-The complex number in the polar form is r(cosФ + i sinФ)

* Lets revise how we can find one from the other

- r² = a² + b²

- tanФ = b/a

* Now lets solve the problem

∵ z = 3(cos 60° + i sin 60°)

∴ r = 3 and Ф = 60°

∵ cos 60° = 1/2

∵ sin 60 = √3/2

- Substitute these values in z

∴ z = 3(1/2 + i √3/2) ⇒ open the bracket

∴ z = 3/2 + i √3/2

* The complex number in the form of a + b i is 3/2 + i √3/2

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.