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How can you use trigonometric functions to simplify # 6 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?

Answer 1

Josiah Anderson

By using Euler's formula.

#6*e^((3π)/8i)=2.2961+5.5433i#

Euler's formula states that:

#e^(ix)=cosx+isinx#

Therefore:

#6*e^((3π)/8i)=6*(cos((3π)/8)+i*sin((3π)/8))=# #=6*(0.3827+0.9239i)=# #=6*0.3827+6*0.9239i=2.2961+5.5433i#

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Answer 2

Adam Aguirre

You can use trigonometric functions to simplify (6 e^{(3 \pi)/8 i}) into a non-exponential complex number by expressing it in trigonometric form.

The expression (e^{(3 \pi)/8 i}) can be written in trigonometric form as (e^{i\theta} = \cos(\theta) + i \sin(\theta)), where (\theta = (3\pi)/8).

Therefore, (6 e^{(3 \pi)/8 i}) can be written as (6(\cos((3\pi)/8) + i\sin((3\pi)/8))).

Now, you can simplify using trigonometric identities to find the cosine and sine of ((3\pi)/8).

Finally, the expression can be written as a non-exponential complex number in the form (a + bi), where (a) is the real part and (b) is the imaginary part.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.