Answered

2i(4+5i)(4-5I)/4+i find the quotient and express it in its simplest form

A; 82/16+32/17i


B: 82/17+328/17i


C: 82/16-308/16i


D: 1/3+11/3i

Verified Answer :

The answer is B, you should really learn how to calculate these yourself though because they come up a lot.

Answer:

\(\frac{82}{17} +\frac{328i}{17}\)

Step-by-step explanation:

\(\frac{2i(4+5i)(4-5i)}{4+i}\)

First we multiply the numerator

(4+5i)(4-5i)= 16+20i-20i -25i^2

the value of i^2=-1

16 - 25(-1)= 16+25= 41

\(\frac{2i(4+5i)(4-5i)}{4+i}\)

\(\frac{2i(41)}{4+i}\)

\(\frac{82i}{4+i}\)

Now multiply the fraction by its conjugate 4-i

\(\frac{82i*(4-i)}{(4+i)(4-i)}\)

\(\frac{328i-82i^2}{4^2-i^2}\)

\(\frac{328i-82(-1)}{16-(-1)}\)

\(\frac{328i+82}{17}\)

\(\frac{82}{17} +\frac{328i}{17}\)

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