Q. Find the modulus and amplitude of the following complex numbers and hence express them into polar form.
1.)      (3 +4i)(4+5i)/(4+3i)(6+7i)

Asked by imabhi264 | 21st Jun, 2017, 10:25: PM

Expert Answer:

begin mathsize 16px style fraction numerator open parentheses 3 plus 4 straight i close parentheses open parentheses 4 plus 5 straight i close parentheses over denominator open parentheses 4 plus 3 straight i close parentheses open parentheses 6 plus 7 straight i close parentheses end fraction
fraction numerator 12 plus 15 straight i plus 16 straight i plus 20 straight i squared over denominator 24 plus 28 straight i plus 18 straight i plus 21 straight i squared end fraction
fraction numerator 12 plus 31 straight i minus 20 over denominator 24 plus 46 straight i minus 21 end fraction space space space space space space space space space space space space space space space space space space space space space space space space open parentheses straight i squared equals negative 1 close parentheses
fraction numerator negative 8 plus 31 straight i over denominator 3 plus 46 straight i end fraction
fraction numerator begin display style negative 8 plus 31 straight i end style over denominator begin display style 3 plus 46 straight i end style end fraction cross times fraction numerator 3 minus 46 straight i over denominator 3 minus 46 straight i end fraction
fraction numerator negative 24 plus 368 straight i minus 1426 straight i squared over denominator 9 minus 2116 straight i squared end fraction
fraction numerator negative 24 plus 368 straight i plus 1426 over denominator 9 plus 2116 end fraction space space space space space space space space space space space space space space space space space space space space space open parentheses straight i squared equals negative 1 close parentheses
fraction numerator 1402 plus 368 straight i over denominator 2125 end fraction
1402 over 2125 plus 368 over 2125 straight i
Now space straight a equals fraction numerator begin display style 1402 end style over denominator begin display style 2125 end style end fraction comma space straight b equals fraction numerator begin display style 368 end style over denominator begin display style 2125 end style end fraction
Find space the space polar space form space

We space appreciate space if space you space solve space it space further space and space post space it space to space us.
If space you space ahve space any space doubt space please space send space us space the space snapshot space of space your space steps space
we space will space guide space you space further.
end style

Answered by Sneha shidid | 22nd Jun, 2017, 09:38: AM