- #1
aisha
- 584
- 0
i^57 is simplified to i ?
Is This True For Complex Numbers?
- Thread starter aisha
- Start date
In summary, the conversation discusses the simplification of i^57, which is equivalent to i. The concept of dividing the exponent by 4 and finding a remainder of 1 is used to arrive at the solution. The conversation also acknowledges the complexity of the solution and thanks those who provided help.
- #2
Nonok
- 8
- 0
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
57 is divisible by 3. So, if I remember my calc class then it would be...
-i
(Don't be mad if I am completely wrong though, its just what I remember)
i^3 = -i
i^4 = 1
i^5 = i
57 is divisible by 3. So, if I remember my calc class then it would be...
-i
(Don't be mad if I am completely wrong though, its just what I remember)
- #3
aisha
- 584
- 0
Who is correct lol? i or -i? which one?
OH NO! NOW I am not sure well I divided the exponent by 4 and got a remainder of 1 which made me think that the answer is simply i
hmmm can someone tell us who is right?
Nonok said:
OH NO! NOW I am not sure well I divided the exponent by 4 and got a remainder of 1 which made me think that the answer is simply i
hmmm can someone tell us who is right?
- #4
vladimir69
- 130
- 0
i have to type some stuff to make my message longer
answer is:
i^57=i
answer is:
i^57=i
- #5
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
- 7,220
- 24
aisha said:
This is correct.
[tex]i^{57} = i^{(56+1)} = i^{56}*i = (i^4)^{14}*i = 1^{14}*i = 1*i = i [/tex]
Last edited:
- #6
Nonok
- 8
- 0
Oh, so there has to be a remainder of 1, guess I forgot that.
Sorry.
Sorry.
- #7
aisha
- 584
- 0
Gokul43201 said:
WOW GOKU ur answer is COMPLEX! lol
holy made me think! A simple question but a long way of simplifying it. Thanks soooo much yayay I got it right. Thanks everyone else for ur help!
FAQ: Is This True For Complex Numbers?
What are complex numbers and why are they important?
Complex numbers are numbers that have both a real and imaginary component. They are important because they allow us to represent and solve mathematical problems that cannot be solved with real numbers alone. They have applications in many fields, including physics, engineering, and computer science.
How are complex numbers represented?
Complex numbers are typically represented in the form a + bi, where a is the real component and bi is the imaginary component. The letter i represents the imaginary unit, which is defined as the square root of -1.
What operations can be performed with complex numbers?
Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. In addition, they have their own set of rules for exponentiation and logarithms. These operations are used to solve complex equations and model real-world phenomena.
Can complex numbers be graphed?
Yes, complex numbers can be graphed on a 2-dimensional plane called the complex plane. The horizontal axis represents the real component, while the vertical axis represents the imaginary component. This allows us to visually represent complex numbers and their relationships.
What is the significance of the complex conjugate?
The complex conjugate of a complex number is another complex number with the same real component but opposite imaginary component. It is denoted by adding a bar over the number, such as z̅. The complex conjugate is useful in simplifying complex equations and finding the modulus (absolute value) of a complex number.
Similar threads
Insights
Views On Complex Numbers