How can I express the complex number in the form of a + bi for the expression 3cos(60°) + i sin(60°)?

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To express the complex number given by the expression 3cos(60°) + i sin(60°) in the form a + bi, we need to evaluate the trigonometric functions involved in the expression.

First, let’s determine the values of the cosine and sine functions for 60 degrees:

  • cos(60°) = 1/2
  • sin(60°) = √3/2

Now we can substitute these values back into the expression:

  • 3cos(60°) = 3 × (1/2) = 3/2
  • i sin(60°) = i × (√3/2) = (√3/2)i

Now we can combine these results:

3cos(60°) + i sin(60°) = (3/2) + (√3/2)i

Thus, the complex number in the form a + bi is:

(3/2) + (√3/2)i

In summary, the complex expression you began with translates neatly into the standard format of a complex number as:

(3/2) + (√3/2)i.

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