मराठी

Find the Value of the Following Expression:I5 + I10 + I15

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प्रश्न

Find the value of the following expression:

i5 + i10 + i15

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उत्तर

\[ i^5 + i^{10} + i^{15} \]

\[ = i^{4 \times 1 + 1} + i^{4 \times 2 + 2} + i^{4 \times 3 + 3} \]

\[ = \left\{ \left( i^4 \right)^1 \times i \right\} + \left\{ \left( i^4 \right)^2 \times i^2 \right\} + \left\{ \left( i^4 \right)^3 \times i^3 \right\}\]

\[ = i + i^2 + i^3 \left[ \because i^4 = 1 \right]\]

\[ = i - 1 - i \left[ \because i^2 = - 1, i^3 = - i \right] \]

\[ = - 1\]

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पाठ 13: Complex Numbers - Exercise 13.1 [पृष्ठ ४]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 13 Complex Numbers
Exercise 13.1 | Q 3.4 | पृष्ठ ४

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