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Simplify the following and express in the form a + ib: (1+2/๐‘–)โข(3+4/๐‘–)โข(5+๐‘–)โˆ’1

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Question

Simplify the following and express in the form a + ib:

`(1 + 2/i)(3 + 4/i)(5 + i)^-1`

Sum
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Solution

`(1 + 2/i)(3 + 4/i)(5 + i)^-1`

= `((i + 2))/i*((3i + 4))/i*1/(5 + i)`

= `(3i^2 + 4i + 6i + 8)/(i^2(5 + i)`

= `(-3 + 10i + 8)/(-1(5 + i)`      ...[โˆต i2 = – 1]

= `((5 + 10i))/(-(5 + i))`

= `((5 + 10i)(5 - i))/(-(5 + i)(5 - i)`

= `(25 - 5i + 50i - 10i^2)/(-(25 - i^2)`

= `(25+ 45i -10(-1))/(-[25 -(-1)]`

= `(35 +45i)/(-26)`

= `(-35)/26 - 45/26 i`

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Chapter 3: Complex Numbers - MISCELLANEOUS EXERCISE - 3 [Page 42]

APPEARS IN

Balbharati Mathematics and Statistics (Commerce) Part 1 [English] Standard 11 Maharashtra State Board
Chapter 3 Complex Numbers
MISCELLANEOUS EXERCISE - 3 | Q 3) vii) | Page 42

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