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Question
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
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Solution
(x + iy) (5 + 6i) = 2 + 3i
∴ x + iy = `(2 + 3"i")/(5 + 6"i")`
∴ x + iy = `((2 + 3"i")(5 - 6"i"))/((5 + 6"i")(5 - 6"i"))`
= `(10 - 12"i" + 15"i" - 18"i"^2)/(25 - 36"i"^2)`
= `(10 + 3"i" - 18(-1))/(25 - 36(-1))`
∴ x + iy = `(28 + 3"i")/61`
= `28/61 + 3/61"i"`
Equating real and imaginary parts, we get
x = `28/61` and y = `3/61`
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