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Simplify the following and express in the form a + ib: 3i5+2i7+i9i6+2i8+3i18 - Mathematics and Statistics

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Sum

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

`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`

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Solution

`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`

= `(3("i"^4*"i")  2("i"^4*"i"^3) + ("i"^4)^2*"i")/("i"^4*"i"^2 + 2("i"^4)+ 3("i"^2)^9)`

= `(3(1)* "i" + 2(1)(- "i") + (1)^2 * "i")/((1)(-1) + 2(1)^2 + 3(-1)^9)`     ...[∵ i2 = –1 , i3 = – i, i4 = 1]

= `(3"i" - 2"i" + "i")/(-1 + 2 - 3)`

= `(2"i")/(-2)`

= – i = 0 – i

Concept: Algebra of Complex Numbers
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Miscellaneous Exercise 3 | Q 3. (ix) | Page 43
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