1. ## Complex Number Problem

|2e^(i*theta) - i |
|______________|
|
|ie^(i*theta) + 2 |

so 2 multiplied by euler to the power of i * theta all subtracted by i divided by i mulitplied by euler to the power of i * theta added by 2

this is all in abs. value the question asks to "Find"

P.S sry i dont know how to make it look all nice and math like

2. Originally Posted by Hamm
|2e^(i*theta) - i |
|______________|
|
|ie^(i*theta) + 2 |

so 2 multiplied by euler to the power of i * theta all subtracted by i divided by i mulitplied by euler to the power of i * theta added by 2

this is all in abs. value the question asks to "Find"

P.S sry i dont know how to make it look all nice and math like
Let $\displaystyle z = \frac{2 e^{i \theta} - i}{i e^{i \theta} + 2}$.
Then
$\displaystyle |z|^2 = z \overline{z} = \frac{2 e^{i \theta} - i}{i e^{i \theta} + 2} \cdot \frac{2 e^{-i \theta} + i}{-i e^{-i \theta} + 2}$

Multiply it out and simplify-- I think you will find the answer to be very simple.

3. thank you very much!