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Question

The real value of 'a' for which 3i3 – 2ai2 + (1 – a) i + 5 is real is ____________.

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Solution

3i3 – 2ai2 + (1 – a) i + 5
i.e 3i2 i – 2a(–1) + (1 – a) i + 5
i.e 3i + 2a + (1 – a) i + 5
i.e 2a + 5 + i(1 – a – 3)
i.e 2a + 5 + i (–a – 2)
Since the above expression is given to be real
⇒ –a – 2 = 0
⇒ a = – 2

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