I think I'm missing something in this complex number problem

[JR Sauerland]

As you can see, it says that -1¹⁰ (-1 to the tenth is just -1), multiplied by i, is somehow i. Everywhere I have looked, -1 times i is negative i, but this problem disagrees. Am I missing something?

 

[micromass]

$(-1)^{10} = 1$

 

[JR Sauerland]

$(-1)^{10} = 1$

But how? Every calculator or form I put it into says it is -1...? EDIT: If I put -1¹⁰ in my graphic calculator, it brings back -1. If I do it as (-1)¹⁰, it says 1. Witchcraft! I am so confused .

 

[micromass]

There is a difference between $-1^{10}$, which is apparently what the calculators are doing and $(-1)^{10}$.

 

[JR Sauerland]

There is a difference between $-1^{10}$, which is apparently what the calculators are doing and $(-1)^{10}$.

What is the difference though?

 

[micromass]

For example:

$$(-1)^4 = (-1)\cdot (-1)\cdot (-1)\cdot (-1) = 1$$

while

$$-1^4 = - (1\cdot 1\cdot 1\cdot 1) = -1$$

 

[JR Sauerland]

For example:

$$(-1)^4 = (-1)\cdot (-1)\cdot (-1)\cdot (-1) = 1$$

while

$$-1^4 = - (1\cdot 1\cdot 1\cdot 1) = -1$$

That was perfect! Thank you so much!

 

[jedishrfu]

Raising a power by convention has higher precedence over multiplication just as multiplication has a higher precedence over addition. Parentheses allow you to reorder the precedence of operations. These rules are especially good to know when you start programming.

 

[pbuk]

JR you leep asking these questions that show that there are really basic things that you have not grasped. Your calculator does not give you the "right" answer because you do not know what buttons to press. If you do not know without even thinking about it that aný even power of -1 is equal to 1 then you cannot progress your studies. As you seem familiar with Khan Academy, can I suggest that you go RIGHT BACK TO THE BEGINNING and take every class?

 

[FactChecker]

Parentheses are your friends in programming. Use -(1¹⁰) or (-1)¹⁰ to be sure what it is calculating exactly what you want it to.