Question

Write the conjugate of (2 + 3i) (1 – 2i) in the form a + i b, a, b e R.​

Answer 1

Answer:

(2 + 3i) (1 – 2i)= 2 - 4i + 3i - 6i^2

(i^2= -1)

= 2-i -6(-1)

= 2 + 6 - I

= 8 - i

but as conjugate of z^- = z ( a + ib ) is the conjugate of (a-ib)

hence , answer = 8 + i

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Answer 2

If $z = a + ib$, then conjugate is $z^-=a-ib$,

$(2 + 3i) (1-2i)= 2 - 4i + 3i - 6i^2$        $(i^2= -1)$

$= 2-i -6(-1)\\= 2 + 6 - i\\= 8 - i$

Conjugate of $z^- = 8+i$.