Question -
Answer -
(i) 1 – i
Given:
1 – i
We know themultiplicative inverse of a complex number (Z) is Z-1 or 1/Z
So,
∴ The multiplicativeinverse of (1 – i) is (1 + i)/2
(ii) (1 + i √3)2
Given:
(1 + i √3)2
Z = (1 + i √3)2
= 12 +(i √3)2 + 2 (1) (i√3)
= 1 + 3i2 +2 i√3
= 1 + 3(-1) + 2 i√3[since, i2 = -1]
= 1 – 3 + 2 i√3
= -2 + 2 i√3
We know themultiplicative inverse of a complex number (Z) is Z-1 or 1/Z
So,
Z = -2 + 2 i√3
∴ The multiplicativeinverse of (1 + i√3)2 is (-1-i√3)/8
(iii) 4 – 3i
Given:
4 – 3i
We know themultiplicative inverse of a complex number (Z) is Z-1 or 1/Z
So,
Z = 4 – 3i
∴ The multiplicativeinverse of (4 – 3i) is (4 + 3i)/25
(iv) √5 + 3i
Given:
√5 + 3i
We know themultiplicative inverse of a complex number (Z) is Z-1 or 1/Z
So,
Z = √5 + 3i
∴ The multiplicativeinverse of (√5 + 3i) is (√5 – 3i)/14
