SOLUTION: • Let x = r(cos u + i sin u)
• Let y = t(cos v + i sin v)
Prove that xy = rt(cos(u+v) + i sin(u+v)) and prove that
The radius (or modulus) of the product xy is rt
I ha
Question 896411: • Let x = r(cos u + i sin u)
• Let y = t(cos v + i sin v)
Prove that xy = rt(cos(u+v) + i sin(u+v)) and prove that
The radius (or modulus) of the product xy is rt
I have to solve and justify the steps. I know that I will plug in the cos u.... and cos v... I have read the chapter and stared at the work for awhile but I am not getting anywhere! Found 2 solutions by jim_thompson5910, Edwin McCravy:Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website! • Let x = r(cos u + i sin u)
• Let y = t(cos v + i sin v)
Prove that xy = rt(cos(u+v) + i sin(u+v)) and prove that
The radius (or modulus) of the product xy is rt
I have to solve and justify the steps. I know that I will plug in the cos u.... and cos v... I have read the chapter and stared at the work for awhile but I am not getting anywhere!
Multiply equals by equals:
Use FOIL
since
factor i out of the middle two terms
Move the last term next to the first term:
Use double angle formulas
and
You might swap the terms of the imaginary part:
and you have:
Edwin