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

Gold Member
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?

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

• aikismos
Gold Member
##(-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 .   There is a difference between ##-1^{10}##, which is apparently what the calculators are doing and ##(-1)^{10}##.

Gold Member
There is a difference between ##-1^{10}##, which is apparently what the calculators are doing and ##(-1)^{10}##.
What is the difference though?

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
Gold Member
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
Mentor
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.

• JR Sauerland and aikismos
pbuk
Gold Member
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?

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• Qwertywerty and micromass
FactChecker
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