How can you use trigonometric functions to simplify # 3 e^( ( pi)/8 i ) # into a non-exponential complex number?
By signing up, you agree to our Terms of Service and Privacy Policy
To simplify (3 \cdot e^{\frac{\pi}{8}i}) into a non-exponential complex number, we can use Euler's formula, which states that (e^{ix} = \cos(x) + i\sin(x)).
Given (e^{\frac{\pi}{8}i}), we can rewrite it as (e^{i\frac{\pi}{8}} = \cos\left(\frac{\pi}{8}\right) + i\sin\left(\frac{\pi}{8}\right)).
Now, substitute this expression into (3 \cdot e^{\frac{\pi}{8}i}):
(3 \cdot e^{\frac{\pi}{8}i} = 3 \cdot \left(\cos\left(\frac{\pi}{8}\right) + i\sin\left(\frac{\pi}{8}\right)\right)).
Thus, the simplified non-exponential complex number is (3 \cdot \left(\cos\left(\frac{\pi}{8}\right) + i\sin\left(\frac{\pi}{8}\right)\right)).
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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.
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.
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.
- What is the distance the polar coordinates #(-2 ,( -3 )/8 )# and #(6 ,(-7 pi )/4 )#?
- How do you evaluate # e^( ( pi)/4 i) - e^( ( 7 pi)/4 i)# using trigonometric functions?
- There is a clown's face on the top of a spinner. The tip of his hat rotates to #(-2, 5)# during one spin. What is the cosine value of this function?
- How do you graph #r=-8cos2theta#?
- How do you write the trigonometric form in complex form #5(cos((3pi)/4)+isin((3pi)/4)))#?
![Answer Background](/cdn/public/images/tutorgpt/ai-tutor/answer-ad-bg.png)
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7