Conjugates in exponential form

In summary, conjugates in exponential form are two expressions related by a change in the sign of the imaginary component. They are important for simplifying complex expressions and performing operations with imaginary numbers. To multiply conjugates, you multiply the real components and subtract the product of the imaginary components. Conjugates can also be divided by multiplying the numerator and denominator by the conjugate of the denominator. They are commonly used in solving equations with complex numbers and finding roots.
  • #1
shannon
11
0

Homework Statement


Show that (ez)*=ez*

note: * is the conjugate


Homework Equations





The Attempt at a Solution


So I wasn't sure what form to put this in...either in exponential re or cos Ѳ + isin Ѳ...Either way, I think I'm just making it too easy...
Please help!
 
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  • #2
you could write z = x + iy and use (z z`)* = z* z`*
 

Related to Conjugates in exponential form

1. What are conjugates in exponential form?

In exponential form, conjugates are two expressions that are related by a change in the sign of the imaginary component. For example, in the expression (a + bi), the conjugate would be (a - bi).

2. Why are conjugates important in exponential form?

Conjugates are important because they allow us to simplify complex expressions and perform operations involving imaginary numbers. They also help us rationalize denominators in complex fractions.

3. How do you multiply conjugates in exponential form?

To multiply conjugates in exponential form, you simply multiply the real components and then subtract the product of the imaginary components. For example, (a + bi)(a - bi) = a^2 + abi - abi - b^2i^2 = a^2 - b^2i^2 = a^2 + b^2.

4. Can you divide conjugates in exponential form?

Yes, you can divide conjugates in exponential form. To do this, you multiply the numerator and denominator by the conjugate of the denominator. This will eliminate the imaginary component in the denominator, allowing you to simplify the expression.

5. How are conjugates used in solving equations with complex numbers?

Conjugates are commonly used in solving equations with complex numbers as they allow us to eliminate the imaginary component and solve for the real solution. They are also used in the process of finding roots of complex numbers.

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