1. ## calculating complex number

Calculate ${i}^{\frac{3}{4}}$

I tried with

$i=cos\frac{pi}{2}+isin\frac{\pi}{2}$

$i^3=cos\frac{3pi}{2}+isin\frac{3\pi}{2}$

$i^3=-i$

$\sqrt[4]{i^3}=\sqrt[4]{-i}$

What should I do next?

2. It would be a lot easier if you started with i=e^(i.pi(2n+1/2)) (.= multiply, n is any integer)

Then i^3/4=e^(i.pi(3n/2 + 3/8)). You will have 4 distinct results for n=0,1,2,3.

3. Ok, thank you..

4. Modulus is one so DeMoivre's Theorem should yield ...
i^ [3/4] = cos [3 pi / 8] + i sin [3 pi / 8]

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•