Simplify and write the complex numbers in the form a + bi, where a and b are real

Re: Simplify and write the complex numbers in the form a + bi, where a and b are real

Can you simplify the 4 expressions below? If so, then do them. Then plug them into your problem.

If not, then which of them confuse you?

$\displaystyle i^{11} = ? \ \ i^{3}= ? \ \ \frac{1}{i^{20}} = ? \ \ i^{-1} = ?$

Re: Simplify and write the complex numbers in the form a + bi, where a and b are real

If i knew that i would already finished that. I only know basic complex numbers. i have no idea how to solve them when its i^x

Re: Simplify and write the complex numbers in the form a + bi, where a and b are real

Quote:

Originally Posted by

**ilovemymath** If i knew that i would already finished that. I only know basic complex numbers. i have no idea how to solve them when its i^x

$\displaystyle i^1=i,~i^2=-1,~i^3=-i,~\&~i^4=1$

If $\displaystyle n>0~\&~n=4k+j$ then $\displaystyle i^n=i^j$. Example $\displaystyle i^{87}=i^3=-i$.

If $\displaystyle \frac{1}{i^n}=(-i)^n$. Eample $\displaystyle \frac{1}{i^9}=(-i)^9=-i$.