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प्रश्न
Find the rectangular form of the complex numbers
`(cos pi/6 "i" sin pi/6)(cos pi/12 + "i" sin pi/12)`
उत्तर
`(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)`
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