CBSE - Maths - Class 11 - Complex Numbers & Quadratic Equations

Assignment Class XI

Complex Numbers and Quadratic Equations

1
Q1. Prove that: (i ) i104  i109  i114  i119  0 (ii ) (1  i )4 (1  ) 4 16
i
1 1 1 1
(iii ) 6i 54  5i 37  2i11  6i 68  7i (iv )  2  3  4  0
i i i i

Q2. Solve for x and y


( x 1) ( y 1)
(i ) (3  i ) x  (1  2i ) y  7i  0 (ii )  i (iii ) (1  i ) y 2  ( 6  i )  ( 2  i ) x
(3  i ) ( 3  i )


Q3. Express the following in the form of x  iy :

(2  3i )2 (1  i )3 3i 3i 3  2i 3  2i
(i ) (ii ) (iii )  (iv ) 
1 i 1 i3 2i 2i 2  3i 2  3i

3 2 2 1 5  2i  1 3  3  4i 
(v )  
1  i 2  i 1 i

(vi) 1  3i  (vii)
1  2i
(viii)    
 1  2i 1  i  2  4i 

Q4. Find the multiplicative inverse of the following:

2  3i ( i  1) ( i  2)
(i ) (ii ) (2  5i )2 (iii ) (6  5i )2 (iv )
3  2i ( i 1) ( i  2)
Q5. Express the following numbers in the polar form:
5i
(i )1  3 i (ii )  1  3 i (iii )  4  4 3 i (iv )
2  3i

1  3i 2  6 3i
(v ) (vi) (vii) 3 2  3 2i
1  2i 5  3i


Q 6. Find the square roots of the following complex numbers:
(i ) 3  4 i (ii ) 5  12i (iii ) 7  24 i (iv )12  5i

(v)8 15 i (vi) 16  30i (vii) 48 14i (viii) 11  60 1


Q7. (i ) If x  3  2i , find the value of x 4  4 x 3  4 x 2  8 x  44 .


1 i
(ii ) If x  , find the value of x 6  x 4  x 2  1 .
2


(iii) If x  4  7i find value of x 3  4 x 2  9 x  97