Forum

Complex Numbers and Quadratic Equations

Evaluate:
3
25
18 1
i
i
      +        
.

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

If x + iy =
a ib
a ib
+

, prove that x
2
+ y
2
= 1.

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Find the conjugate of
(3 2 )(2 3 )
(1 2 )(2 )

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Find the multiplicative inverse of each of the complex numbers given in the
Exercises 11 to 13.
11. 4 – 3i 12. 5 3 + i 13. – i
14. Express the following expression in the form of a + ib :
( ) ( )
( ) ( )

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Express each of the complex number given in the Exercises 1 to 10 in the
form a + ib.
4. 3(7 + i7) + i (7 + i7) 5. (1 – i) – ( –1 + i6)
6.
1 2 5 4
5 5 2
i i         + − +     7.
1 7 1 4 4
3 3 3 3
i i i
      
      + + + − − +  
      
8. (1 – i)
4 9.
3
1
3
3
i
    +
  10.
3
1
2
3
i
    − −  

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Express each of the complex number given in the Exercises 1 to 10 in the
form a + ib.
4. 3(7 + i7) + i (7 + i7) 5. (1 – i) – ( –1 + i6)
6.
1 2 5 4
5 5 2
i i         + − +     7.
1 7 1 4 4
3 3 3 3
i i i
      
      + + + − − +  
      
8. (1 – i)
4 9.
3
1
3
3
i
    +
  10.
3
1
2
3
i
    − −  

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Express each of the complex number given in the Exercises 1 to 10 in the
form a + ib.
1. ( ) 3
5
5
i i  
−    2. i i
9 19
+ 3. i
−39

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Express the following in the form a + ib
(i)
5 2
1 2
i
i
+

(ii) i–35

03/11/2024

Mathematics

11th (Science)

Complex Numbers and Quadratic Equations

Find the multiplicative inverse of 2 – 3i.

03/11/2024

Mathematics

11th (Science)

Complex Numbers – Modulus and Argument

If z equals 3 plus 4i, calculate the modulus and argument of the complex number z.

02/11/2024

Mathematics

12th (Science)