# Thread: Algebra2 - Complex Numbers

1. ## Algebra2 - Complex Numbers

I'm currently struggling with complex numbers alot, and dont really know where to start. Any help would be much appreciated.

Write the complex number i^15 in the usual a + bi form;

Write the complex number 2-i/5+i in the usual a + bi form

2. Well, $i^{15} = -i$ so:

$i^{15} = 0 + -1(i) = 0 - i$ (If it MUST be in a + bi, then use 0 + -i, if not, then use 0 - i or just -i).

$2 - \frac{i}{5} + i$

$2 - \frac{i}{5} + \frac{5i}{5} = 2 - \frac{4i}{5}$

In a + bi form:

$2 + -\frac{4}{5}i$

3. Originally Posted by 14041471
Write the complex number 2-i/5+i in the usual a + bi form
My guess is you meant this:

$\frac{2-i}{5+i}$

But I could be wrong.

$\frac{2-i}{5+i} \cdot \frac{5-i}{5-i}=\frac{10-5i-2i+1}{25+1}=\frac{11-7i}{26}=\frac{11}{26}-\frac{7}{26}i$

4. ## Thanks

You were right. Thanks
Originally Posted by masters
My guess is you meant this:

$\frac{2-i}{5+i}$

But I could be wrong.

$\frac{2-i}{5+i} \cdot \frac{5-i}{5-i}=\frac{10-5i-2i+1}{25+1}=\frac{11-7i}{26}=\frac{11}{26}-\frac{7}{26}i$