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Question
Find a and b if `1/("a" + "ib")` = 3 – 2i
Solution
`1/("a" + "ib")` = 3 – 2i
∴ a + ib = `1/(3 - 2"i")`
∴ a + ib = `1/(3 - 2"i") xx (3 + 2"i")/(3 + 2"i")`
∴ a + ib = `(3 + 2"i")/(9 - 4"i"^2)`
∴ a + ib = `(3 + 2"i")/(9 + 4)` ...[∵ i2 = – 1]
∴ a + ib = `(3 + 2"i")/13 = 3/13 + 2/13 "i"`
Equating the real and imaginary parts separately, we get,
a = `3/13`, b = `2/13`
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