Question

Simplify:

i4 + i3 + i2 + i

Answer 1

\[\Large i=\sqrt{-1}\]assuming?

Answer 2

are these exponents?

Answer 3

\[i^4 + i^3 + i^2 + i\]

Answer 4

satellite, what is the trend for i? i forgot and dont have my notes, i know it goes in set of 4, so 1i, 2i, 3i,4i then repeats. so would you know what im speaking about?

Answer 5

no, no exponents,
The answer choices are
A) 0
B) 1
C) -1
D) i

Answer 6

then i am going to guess they are exponents
in fact i am sure they are

Answer 7

@sjerman1 the pattern is
\[i^0=1, i^1=i, i^2=-1, i^3=-i, i^4=1, ...\]

Answer 8

*YES! sorry about that. They're exponents.

Answer 9

thank you, this will help @Charles10 quite a bit.
@Charles10 WRITE THAT DOWN

Answer 10

@Charles10 compute as i wrote above

Answer 11

i did, i appreciate it. @satellite73 @sjerman1

Answer 12

They are exponents, you are @satellite73

Remember, complex numbers with imaginary parts are added the same way complex numbers without imaginary parts (Real Numbers). Similarly, imaginary parts are raised to powers the same way. This gives:\[i = \sqrt{-1} \rightarrow i^4 +i^3+i^2+i=(\sqrt{-1})^4+(\sqrt{-1})^3+(\sqrt{-1})^2+\sqrt{-1}\]\[(-1)(-1)+(-1\sqrt{-1})+(-1)+\sqrt{-1}=1-\sqrt{-1}-1+\sqrt{-1}=0\]Get it?
@Charles10

Answer 13

They are exponents, you are @satellite73

Remember, complex numbers with imaginary parts are added the same way complex numbers without imaginary parts (Real Numbers). Similarly, imaginary parts are raised to powers the same way. This gives:\[i = \sqrt{-1} \rightarrow i^4 +i^3+i^2+i=(\sqrt{-1})^4+(\sqrt{-1})^3+(\sqrt{-1})^2+\sqrt{-1}\]\[(-1)(-1)+(-1\sqrt{-1})+(-1)+\sqrt{-1}=1-\sqrt{-1}-1+\sqrt{-1}=0\]Get it?
@Charles10

Answer 14

They are exponents, you are @satellite73

Remember, complex numbers with imaginary parts are added the same way complex numbers without imaginary parts (Real Numbers). Similarly, imaginary parts are raised to powers the same way. This gives:\[i = \sqrt{-1} \rightarrow i^4 +i^3+i^2+i=(\sqrt{-1})^4+(\sqrt{-1})^3+(\sqrt{-1})^2+\sqrt{-1}\]\[(-1)(-1)+(-1\sqrt{-1})+(-1)+\sqrt{-1}=1-\sqrt{-1}-1+\sqrt{-1}=0\]Get it?
@Charles10