Home
Class 11
MATHS
Write down the conjugate of each of the ...

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

Text Solution

Verified by Experts

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)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the multiplicative inverse of each of the following : (i)" "sqrt(5)+3i" "(ii)" "4-3i" "(iii)" "(3i-1)^(2)" "(iv)" "-i

Write the conjugate of the following numbers: sqrt(5)-i and sqrt(2)+sqrt(3)i

Find the multiplicative inverse of each of the following : (i)" "(1-sqrt(3)i)" "(ii)" "(2+5i)" "(iii)" "((2+3i))/((1+i))" "(iv)" "((1+i)(1+2i))/((1+3i))

Write the conjugate base of the following : " (i) " NH_(3) " (ii) " HF " (iii) " H_(3)PO_(4) " (iv) " HS^(-).

Find the square roots of the following: (i) 3-4sqrt(7)i (ii) 4+6sqrt(-5) (iii) -2+2sqrt(3)i .

Write the abscissa of each of the following points: (i) (0, 5) (ii) (3, 7) (iii) (-2, 4) (iv) (6, -3)

Find the principal value of each of the following: i) sin^(-1)(1/sqrt(2)) ii) cos^(-1)(sqrt(3))/2 iii) tan^(-1)(sqrt(3)) iv) "cosec"^(-1)(2)

Rationalise the denominator of each the of the following : (i)(1)/(3+sqrt(5))" "(ii)(1)/(sqrt(5)-sqrt(3))" "(iii)(16)/(sqrt(41)+5)" "(iv)(30)/(5sqrt(3)+3sqrt(5))" "(v)(3-2sqrt(2))/(3+2sqrt(2))

Rationalise the denominator of each the following (i)(2)/(sqrt(3))" "(ii)(1)/(3sqrt(5))" "(iii)(1)/(sqrt(8))" "(iv)(sqrt(2)+1)/(sqrt(3))