How is exp(i*Pi/4) related to (1+i)/sqrt2?

Thread starter Chronos000
Start date Apr 1, 2011
Tags

Exponential

In summary, to rearrange an exponential equation, you can take the logarithm of both sides to bring the exponential term down to the base and solve for the variable. The purpose of rearranging an exponential equation is to make it easier to solve or compare, and to simplify complicated expressions. Any exponential equation can be rearranged as long as you follow the proper steps and maintain equality. When handling negative exponents, you can use the property a^(-n) = 1/a^n to rewrite the equation with positive exponents. Common mistakes to avoid when rearranging an exponential equation include forgetting to take the logarithm of both sides, and not using the correct properties of exponents.

Apr 1, 2011

Chronos000

Homework Statement

I need to use the relation exp(i*Pi/4) = (1+i)/sqrt2 but I'd like to know where it came from. I am clueless about how to arrive at this.

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Apr 1, 2011

Mark44

Mentor

Insights Author

What you're looking for is this identity:
[tex]e^{i x} = cos(x) + i sin(x)[/tex]

Apr 1, 2011

Chronos000

ah, so simple, thanks

Related to How is exp(i*Pi/4) related to (1+i)/sqrt2?

1. How do you rearrange an exponential equation?

To rearrange an exponential equation, you can take the logarithm of both sides. This will bring the exponential term down to the base and allow you to solve for the variable.

2. What is the purpose of rearranging an exponential equation?

Rearranging an exponential equation can make it easier to solve for a variable or to compare different equations. It can also help to simplify complicated expressions.

3. Can you rearrange any exponential equation?

Yes, any exponential equation can be rearranged as long as you follow the proper steps and maintain the equality of both sides.

4. How do you handle negative exponents when rearranging an exponential equation?

To handle negative exponents when rearranging an exponential equation, you can use the property that a^(-n) = 1/a^n. This will allow you to rewrite the equation with positive exponents.

5. Are there any common mistakes to avoid when rearranging an exponential equation?

Yes, one common mistake is forgetting to take the logarithm of both sides when rearranging an exponential equation. Another mistake is not using the correct properties of exponents, such as forgetting the negative exponent rule or the power rule.