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

1. Aug 2, 2015

### 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?

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2. Aug 2, 2015

### micromass

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

3. Aug 2, 2015

### JR Sauerland

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 .

4. Aug 2, 2015

### micromass

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

5. Aug 2, 2015

### JR Sauerland

What is the difference though?

6. Aug 2, 2015

### micromass

Staff Emeritus
For example:

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

while

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

7. Aug 2, 2015

### JR Sauerland

That was perfect! Thank you so much!!

8. Aug 2, 2015

### Staff: 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.

9. Aug 2, 2015

### MrAnchovy

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?

Last edited: Aug 2, 2015
10. Aug 3, 2015

### 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.