Q. 1 E4.2( 9 Votes )

Simplify each of the following and express it in the form a + ib :

(1 – i)2 (1 + i) – (3 – 4i)2

Answer :

Given: (1 – i)2 (1 + i) – (3 – 4i)2

= (1 + i2 – 2i)(1 + i) – (9 + 16i2 – 24i)


[(a – b)2 = a2 + b2 – 2ab]


= (1 – 1 – 2i)(1 + i) – (9 – 16 – 24i) [ i2 = -1]


= (-2i)(1 + i) – (- 7 – 24i)


Now, we open the brackets


-2i × 1 – 2i × i + 7 + 24i


= -2i – 2i2 + 7 + 24i


= -2(-1) + 7 + 22i [, i2 = -1]


= 2 + 7 + 22i


= 9 + 22i



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