Question

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▶ If (1+i)(1+2i)(1+3i)...(1+ni)=(x+iy),show that: 2.5.10 ... (1+n²)=x²+y².

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Answer 1

Answer:

Given (1+i)(1+2i)(1+3i).............(1+ni)=x+iy

⇒|(1+i)(1+2i)(1+3i).............(1+ni)|=|x+iy|

⇒|1+i||1+2i|..........|1+ni|=x2+y2−−−−−−√

⇒2–√5–√10−−√.......1+n2−−−−−√=x2+y2−−−−−−√

squaring on both the sides we get

2.5.10........(1+n2)=x2+y2

Answer 2

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