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The reciprocal of a + bi is a - bi:

1/(a + bi) since the conjugate is a - bi:

= 1(a - bi)/[(a + bi)(a - bi)]

= (a - bi)/[a2 - (b2)(i2)] since i2 equals to -1:

= (a - bi)/(a2 + b2) since a2 + b2 = 1:

= a - bi/1

= a - bi

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Q: What is the reciprocal of a plus bi if a2 plus b2 equals 1?
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