SureDenNCERT Solutions Exercise 1
Question 1: Express the given complex number in the form a + ib: (5i)(-3/5i)
Answer 1:
(5i)(-3/5i)=-5 x (3/5) x i x i
= -3i2
= -3(-1) [i2=-1]
= 3
Question 2: Express the given complex number in the form a + ib: i9 + i19
Answer 2:
i9 +i19 =i4 x 2 +1 + i4 x 4 +3
= (i4)2 . i + (i4)4 x i3
= 1 x I + 1 x (-i) [i4=1, i3=-i]
= i+(-i)
=0
Question 3: Express the given complex number in the form a + ib: i–39
Answer 3:
i-39=i-4 x 9 -3=(i4)-9 . i-3
= (1)-9 . i-3 [i4=1]
= (1/i3)=(1/-i) [i3=-i]
= (-1/i) x (i/i)
= (-i/i2)=(-i/-1)=I [i2=-1]
Question 4: Express the given complex number in the form a + ib:
3(7 + i7) + i(7 + i7)
Answer 4:
3(7 + i7) + i(7 + i7)=21+21i+7i+7i2
= 21+28i+7 x (-1) [Because i2=-1]
= 14+28i
Question 5: Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)
Answer 5:
(1-i)-(-1+i6)=1-i+1-6i
=2-7i
Question 6: Express the given complex number in the form a + ib: 
Answer 6:
Question 7: Express the given complex number in the form a + ib:
Answer 7:
Question 8: Express the given complex number in the form a + ib: (1 – i)4
Answer 8:
(1-i)4=[(1-i)2]2
= [12+i2-2i]2
= [1-1-2i]2
= (-2i)2
= (-2i) x (-2i)
= 4i2 = -4 [i2 =-1]
Question 9: Express the given complex number in the form a + ib: 
Answer 9:
[i3=-i]
[i2=-i]
Question 10: Express the given complex number in the form a + ib: 
Answer 10: 
[i3=-i]
[i2=-i]
Question 11: Find the multiplicative inverse of the complex number 4 – 3i.
Answer 11: Let z = 4 – 3i
Then,
Therefore, the multiplicative inverse of 4 – 3i is given by
Question 12: Find the multiplicative inverse of the complex number 
Answer 12: 
Then, 
Therefore, the multiplicative inverse of
Question 13: Find the multiplicative inverse of the complex number –i
Answer 13: Let z = –i
Then, 
Therefore, the multiplicative inverse of –i is given by
Question 14: Express the following expression in the form of a + ib. 
Answer 14: 
[(a+b)(a-b)=a2+b2]
[i2=-1]
