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To find the multiplicative inverse of a complex number z = (a + bi), divide its complex conjugate z* = (a - bi) by z* multiplied by z (and simplify):

z = 4 + i

z* = 4 - i

multiplicative inverse of z:

z* / (z*z)

= (4 - i) / ((4 - i)(4 + i)

= (4 - i) / (16 + 1)

= (4- i) / 17

= 1/17 (4 - i)

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โˆ™ 2010-04-12 09:21:46
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Q: What is the multiplicative inverse of 4 plus i?
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