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Simplify the following and express in the form a + ib. (1 + 3i)^2 (3 + i)

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Simplify the following and express in the form a + ib.

(1 + 3i)2 (3 + i)

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(1 + 3i)2 (3 + i)

= (1 + 6i + 9i2)(3 + i)

= (1 + 6i – 9)(3 + i) ……[∵ i2 = -1]

= (-8 + 6i)(3 + i)

= -24 – 8i + 18i + 6i2

= -24 + 10i + 6(-1)

= -24 + 10i – 6

= -30 + 10i

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