# Reduce complex exponential expression

• kususe
In summary, the conversation discusses proving the equation 1-exp(-iwt)= 2i*sin(wt/2) by using the equation exp(iwt)= cos(wt) + i*sin(wt) and the duplication expression of trigonometry theory. However, it is discovered that the equation is not true and after considering the additional term exp(-iwt/2), the equivalence is proven.
kususe

## Homework Statement

prove that:
1-exp(-iwt)= 2i*sin(wt/2)

## Homework Equations

exp(iwt)= cos (wt) + i*sin(wt)

## The Attempt at a Solution

I attempted to express the exponential into sum of cos and sin and considering t=2*t/2 in order to obtain an argument like (t/2) (using duplication expression of trigonometry theory).

Thanks in advance

You must have the problem wrong, because the equation you are trying to prove is not true. For example, if wt = pi/2, then the left-hand side is equal to 1+i and the right-hand side is equal to √2 * i.

Yes, you're right and the problem was wrong.
In the right-hand side of first expression, there's also

exp(-iwt/2)

And the equivalence is proved.

Last edited:

## What is a complex exponential expression?

A complex exponential expression is an expression that contains a number raised to a complex number, where a complex number is a number with a real and imaginary component.

## How do you reduce a complex exponential expression?

To reduce a complex exponential expression, you can use the properties of exponents, such as the power rule and product rule, to simplify the expression. You may also need to use basic algebraic rules, such as combining like terms, to fully reduce the expression.

## Can a complex exponential expression be written in a simpler form?

Yes, a complex exponential expression can often be simplified to a simpler form by following the steps for reducing the expression. However, some expressions may not have a simpler form and cannot be further reduced.

## What are some common mistakes to avoid when reducing a complex exponential expression?

Some common mistakes to avoid when reducing a complex exponential expression include forgetting to apply the correct exponent rules, not simplifying fully, and making arithmetic errors. It is important to carefully follow the steps and double-check your work to avoid these mistakes.

## Why is reducing complex exponential expressions important?

Reducing complex exponential expressions is important because it allows us to simplify complicated mathematical expressions and make them easier to work with. This can help us solve equations and better understand the relationships between different numbers and variables in an expression.

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