Respuesta :

Finding the sine and the cosine of the angle, it is found that the complex number in standard form is z = -2.165 + 1.25i.

What is a complex number?

A complex number is given by:

z = a + bi.

In which:

  • a is the real part.
  • b is the imaginary part.

In this problem, the complex number is given by:

[tex]z = \frac{5}{2}(\cos{(150^\circ)} + i\sin{(150^\circ)})[/tex]

Using a calculator, we have that:

  • cos(150º) = -0.866.
  • sin(150º) = 0.5.

Hence:

z = 2.5 x (-0.866) + 2.5 x 0.5i

z = -2.165 + 1.25i.

More can be learned about complex numbers at https://brainly.com/question/25572463

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