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Find the multiplicative inverse of each of the following: (2+5

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Find the multiplicative inverse of each of the following:
$(2 + 5 i)$

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Find the multiplicative inverse of each of the following:

(2 + 5 i)

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Text solutionVerified

Multiplicative inverse of

2 + 5 i = \frac{1}{2 + 5 i}

= \frac{1}{2 + 5 i} \times \frac{2 - 5 i}{2 - 5 i}

= \frac{2 - 5 i}{4 - 25 i ^{2}}

= \frac{2 - 5 i}{29}

= \frac{2}{29} - \frac{5}{29} i

Hence, multiplicative inverse of

2 + 5 i = \frac{2}{29} - \frac{5}{29} i

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Question Text	Find the multiplicative inverse of each of the following: $(2 + 5 i)$
Answer Type	Text solution:1
Upvotes	150