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4-1.Complex numbers
normal
${\left( { - \frac{1}{2} + \frac{{\sqrt 3 }}{2}i} \right)^{1000}}\,\, = \,\,\,.....\,\,.$
A
$\frac{1}{2}\,\, + \,\,\frac{{\sqrt 3 }}{2}i$
B
$\frac{1}{2}\,\, - \,\,\frac{{\sqrt 3 }}{2}i$
C
$ - \frac{1}{2}\,\, + \,\,\frac{{\sqrt 3 }}{2}i\,\, = \,\,\,\omega $
D
આમાંથી એક પણ નહિ.
Solution
અહીં $,\,\, – \frac{1}{2}\,\, + \,\,\frac{{\sqrt 3 }}{2}i\,\, = \,\,\,\omega \,$ એ $1$ નું ધનમૂળ છે.
હવે, $\,\,{\left( { – \frac{1}{2}\, + \,\frac{{\sqrt 3 }}{2}i} \right)^{1000}}$
$ = \,\,{\omega ^{1000}}\,\,\,\, = \,\,{({\omega ^3})^{333}}.$
$\omega \,\,\, = \,\,1\,.\,\,\omega \,\,\, = \,\,\omega \,\,\, = \,\, – \frac{1}{2}\,\, + \,\,\frac{{\sqrt 3 }}{2}i$
Standard 11
Mathematics
