Express the following in the form of a + ib, a, b ∈ R, i = -1. State the values of a and b: 3+2i2-5i+3-2i2+5i - Mathematics and Statistics

Sum

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: `(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i")`

`(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i")`

= `((3 + 2"i")(2 + 5"i") + (2 - 5"i")(3 - 2"i"))/((2 - 5"i")(2 + 5"i"))`

= `(6 + 15"i" + 4"i" + 10"i"^2 + 6 - 4"i" - 15"i" + 10"i"^2)/(4 - 25"i"^2)`

= `(12 + 20"i"^2)/(4 - 25"i"^2)`

= `(12 + 20(-1))/(4 - 25(-1))` ...[∵ i² = – 1]

= `(-8)/(29)`

∴ `(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i") = (-8)/29 + 0"i"`

∴ a = `(-8)/29 and "b"` = 0

Concept: Conjugate of a Complex Number

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Chapter 3 Complex Numbers
Exercise 3.1 | Q 2. (iv) | Page 37