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anonymous

  • 4 years ago

5i/(2+3i)^2 Write the quotient in standard form

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  1. anonymous
    • 4 years ago
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    you will need so square the denomniator first and see what you get

  2. anonymous
    • 4 years ago
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    you should get \[(2+3i)^2=-5+12i\] so your next step is to divide \[\frac{5i}{-5+12i}\]and you do this by multiplying numerator and denominator by the conjugate of the denominator, in other words multiply by \[\frac{-5-12i}{-5-12I}\]

  3. anonymous
    • 4 years ago
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    the denominator will be \[5^2+12^2=169\] and the numerator will be \[5i(-5-12i)\] or \[-25i+60\] giving your final answer as \[\frac{60}{169}-\frac{25}{19}i\]

  4. anonymous
    • 4 years ago
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    typo on last line \[\frac{60}{169}-\frac{25}{169}i\]

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