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Question
Answer the following:
Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.
Solution
z = `5/((1 - "i")(2 - "i")(3 - "i"))`
= `5/((2 - "i" - 2"i" + "i"^2)(3 - "i"))`
= `5/((2 - 3"i" - 1)(3 - "i"))` ...[∵ i2 = – 1]
= `5/((1 - 3"i")(3 - "i"))`
= `5/(3 - "i" - 9"i" + 3"i"^2`
= `5/(3 - 10"i" - 3)`
= `5/(-10"i")`
= `(5"i")/(-10"i"^2)`
= `(5"i")/10`
= `1/2"i"`, which is a purely imaginary number.
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