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Tamil Nadu Board of Secondary EducationHSC Science Class 12

Find the rectangular form of the complex numbers ii(cos π6 isin π6)(cos π12+isin π12) - Mathematics

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Question

Find the rectangular form of the complex numbers

`(cos  pi/6  "i" sin  pi/6)(cos  pi/12 + "i" sin  pi/12)`

Sum

Solution

`(cos  pi/6  "i" sin  pi/6)(cos  pi/12 + "i" sin  pi/12)`

= `cos  pi/6 cos  pi/12 + "i" cos  pi/6 sin  pi/12 + "i" sin  pi/6 cos  pi/12 - sin  pi/6 sin  pi/12`

= `(cos  pi/6 cos  pi/12 - sin  pi/6 sin  pi/12) + "i"(cos  pi/6 cos  pi/12 + cos  pi/6 sin  pi/12)`

= `cos(pi/6 + pi/12) + "i" sin(pi/6 + pi/12)`

= `cos  pi/4 + "i" sin  pi/4`

= `(1/sqrt(2)) + "i"(1//sqrt(2))`

= `(1 + "i")/sqrt(2)`

Aliter:

`(cos  pi/6  "i" sin  pi/6)(cos  pi/12 + "i" sin  pi/12)`

= `cos(pi/6 + pi/12) + "i" sin(pi/6 + pi/12)`

= `(cos  (3pi)/12 + "i" sin  (3pi)/12)`

= `cos  pi/4 + "i" sin  pi/4`

= `1/sqrt(2) + "i"/sqrt(2)`

= `(1 + "i")/sqrt(2)`

shaalaa.com
Polar and Euler Form of a Complex Number
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Chapter 2: Complex Numbers - Exercise 2.7 [Page 83]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 2 Complex Numbers
Exercise 2.7 | Q 2. (i) | Page 83

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