1)Express the complex number i⁹ + i¹⁹ in the form of a + ib 2) Find multiplicative Inverse of 4 – 3i​

Question

1)Express the complex number i⁹ + i¹⁹ in the form of a + ib
2) Find multiplicative Inverse of 4 – 3i​

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Camila 2 weeks 2021-10-08T06:25:36+00:00 1 Answer 0 views 0

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    2021-10-08T06:26:53+00:00

    \underline{\underline{\blue{\textbf{Step - By - Step - Explanation : -}}}}

    (i) Express the complex number i⁹ + i¹⁹ in the form of a + ib .

    Solution :

     \rm  =  {i}^{9}  +  {i}^{19}

    \rm  = ( {i}^{2}  {)}^{4}  \times i +  ({i}^{2}  {)}^{9}  \times i

    we know that,

    • i² = -1

    \rm  = ( - 1) {}^{4}  \times i + ( - 1) ^{9}  \times i

    \rm  =  1 \times i + ( - 1) \times i

    \rm  = i - i

    \rm  = 0

    ━━━━━━━━━━━━━━━━━━━━━━━

    (ii) Find multiplicative Inverse of 4 – 3i

    = 1/(4 – 3i)

    • Rationalising the denominator :

    = 1/(4 – 3i) × (4 + 3i)/(4 + 3i)

    = (4 + 3i)/(4 – 3i)(4 + 3i)

    • By using Identity (a + b)(a b) =

    = (4 + 3i)/(4² – (3i)²)

    = (4 + 3i)/(16 + 9)

    = (4 + 3i)/25

    = 4/25 + 3i/25

    ━━━━━━━━━━━━━━━━━━━━━━━━━

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