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(1 + 2i) (2 + 3i) = (1* 2) + (1 * 3i) + (2i * 2) + (2i * 3i)

This gives: 2 + 3i + 4i + 6i

Simplifying the above expression by combining the like terms, we get: 2 + (3i + 4i) + 6i

This gives: 2 + 7i + 6i

The value of i = √-1 ==>i = -1

So we get: 2 + 7i + (6 * -1) ==> 2 + 7i – 6

This simplifies to: 7i – 4

To simplify the given expression, we should multiply the numerator and the denominator by the conjugate of (3 – i) which is (3 + i).

This gives: [4 * (3 + i)]/ [(3 – i) * (3 + i)]

This gives: (12 + 4i)/ (9 – i

The value of i = √-1 ==>i = -1

This implies: (12 + 4i)/ (9 – (-1)) ==> [4 * (3 + i)]/ 10 = [2 * (3 + i)]/ 5

Simplifying further we get: