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Question
Answer the following:
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Solution
`(4 + 3"i")/(1 - "i") = (4 + 3"i")/(1 - "i") xx (1 + "i")/(1 + "i")`
= `(4 + 4"i" + 3"i" + 3"i"^2)/(1 - "i"^2)`
= `(4 + 7"i" - 3)/(1 + 1)` ...[∵ i2 = – 1]
= `(1 + 7"i")/2`
= `1/2 + 7/2"i"`, which is of the form a + bi.
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