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Answer:

It's actually this

Step-by-step explanation

(told it to convert to rectangular form)

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The complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).

What are complex numbers?

Complex numbers are used to define imaginary numbers, that is, the square roots of negative numbers. √-1 is represented as i.

How to solve the question?

In the question, we are given a complex number 5/2(cos 150° + i sin 150°), and are asked to represent it in the form a + bi.

We know that complex numbers can be written in two forms, a + bi or r(cos θ + i sin θ).

The relation between these are:

r² = a² + b²,

a = r cos θ, b = r sin θ,

tan θ = b/a.

So, comparing 5/2(cos 150° + i sin 150°), to r(cos θ + i sin θ), we can say that r = 5/2, and θ = 150°.

Therefore, a = r cos θ = (5/2) cos 150° = (5/2) (-cos 30°) = -(5√3)/4

b = r sin θ = (5/2) sin 150° = (5/2) sin 30° = 5/4.

Therefore, the complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).

Learn more about complex numbers at

https://brainly.com/question/10662770

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