Solving Eigenvalues: Complex Numbers Solutions

[izzy93]

I have solutions for eigenvalues to be

λ1=i-1 = √2 e^i(3∏/4) and
λ2=i+1 =√2 e^i(∏/4)

How do you go from the i-1 to the next bit for both?

Thanks

 

[mfb]

Convert the numbers to their polar form.

 

[izzy93]

Thanks,

Just wondering for λ1=i-1 = √2 e^i(3∏/4) , I get the angle phi to be -∏/4 so if the angle is negative do you take it as a rule to add on ∏?

 

[I like Serena]

Thanks,

Just wondering for λ1=i-1 = √2 e^i(3∏/4) , I get the angle phi to be -∏/4 so if the angle is negative do you take it as a rule to add on ∏?

The angle isn't -∏/4.
If it were, the corresponding expression would be 1 - i.

 

[mathman]

Thanks,

Just wondering for λ1=i-1 = √2 e^i(3∏/4) , I get the angle phi to be -∏/4 so if the angle is negative do you take it as a rule to add on ∏?

You can add 2∏. When you add ∏, you are multiplying by -1.