Question -
Answer -
(i) 4 – 5i
Given:
4 – 5i
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of (4 –5i) is (4 + 5i)
(ii) 1 / (3 + 5i)
Given:
1 / (3 + 5i)
Since the givencomplex number is not in the standard form of (a + ib)
Let us convert tostandard form by multiplying and dividing with (3 – 5i)
We get,
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of (3 –5i)/34 is (3 + 5i)/34
(iii) 1 / (1 + i)
Given:
1 / (1 + i)
Since the givencomplex number is not in the standard form of (a + ib)
Let us convert tostandard form by multiplying and dividing with (1 – i)
We get,
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of(1-i)/2 is (1+i)/2
(iv) (3 – i)2 /(2 + i)
Given:
(3 – i)2 /(2 + i)
Since the givencomplex number is not in the standard form of (a + ib)
Let us convert tostandard form,
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of (2 –4i) is (2 + 4i)
(v) [(1 + i) (2 + i)] / (3+ i)
Given:
[(1 +i) (2 + i)] / (3 + i)
Since the givencomplex number is not in the standard form of (a + ib)
Let us convert tostandard form,
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of (3 +4i)/5 is (3 – 4i)/5
(vi) [(3 – 2i) (2 + 3i)] /[(1 + 2i) (2 – i)]
Given:
[(3 –2i) (2 + 3i)] / [(1 + 2i) (2 – i)]
Since the givencomplex number is not in the standard form of (a + ib)
Let us convert tostandard form,
We know the conjugateof a complex number (a + ib) is (a – ib)
So,
∴ The conjugate of (63– 16i)/25 is (63 + 16i)/25