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).
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