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

• September 25th 2012, 02:07 PM
ilovemymath
Simplify and write the complex numbers in the form a + bi, where a and b are real
3i^11+6i^3+8/i^20+i^−1

• September 25th 2012, 02:22 PM
johnsomeone
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?
$i^{11} = ? \ \ i^{3}= ? \ \ \frac{1}{i^{20}} = ? \ \ i^{-1} = ?$
• September 25th 2012, 02:28 PM
ilovemymath
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
• September 25th 2012, 02:57 PM
Plato
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

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

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

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