Write down the conjugate of each of the following : `(i)" "(-5+sqrt(-1))" "(ii)" "(-6-sqrt(-3))" "(iii)" "i^(3)" "(iv)" "(4+5i)^(2)`

Write down the conjugate of each of the following : `(i)" "(-5+sqrt(-1

1.	Write down the conjugate of each of the following : `(i)" "(-5+sqrt(-1))" "(ii)" "(-6-sqrt(-3))" "(iii)" "i^(3)" "(iv)" "(4+5i)^(2)`
Answer» We know that the conjugate of z = (a + ib) is given as `bar(z) = (a - ib)`. (i) Let `z = -5+sqrt(-1)=(-5+i)`. Then, `bar(z) = bar((-5+i))=(-5-i)`. (ii) Let `z = -6- sqrt(-3) = -6 - i sqrt(3)`. Then, `bar(z) = bar((-6-i sqrt(3))) = (-6 + i sqrt(3))`. (iii) Let `z = i^(3) = -i = 0 - i`. Then, `bar(z)=bar((0-i))=(0+i)=i`. (iv) Let `z = (4+5i)^(2)=(4)^(2) + (5i)^(2)+2 xx 4 xx 5i` `=(16 - 25 + 40i)=(-9+40i)`. `bar(z)=bar((-9+40i))=(-9-40i)`.