Complex Numbers and Quadratic Equations

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  • Complex Numbers and Quadratic Equations Assignments 1

    If, then find the least positive integral value of m.

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  • Complex Numbers and Quadratic Equations Assignments 2

    If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that

    (a2 + b2) (c2 + d2) (e2 + f 2) (g2 + h2) = A2 + B2.

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  • Complex Numbers and Quadratic Equations Assignments 3

    Find the number of non-zero integral solutions of the equation.

     

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  • Complex Numbers and Quadratic Equations Assignments 4

    If α and β are different complex numbers with = 1, then find.

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  • Complex Numbers and Quadratic Equations Assignments 5

    If (x + iy)3 = u + iv, then show that.

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  • Complex Numbers and Quadratic Equations Assignments 6

    Find the modulus of .

     

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  • Complex Numbers and Quadratic Equations Assignments 7

    Find the real numbers x and y if (x - iy) (3 + 5i) is the conjugate of -6 - 24i.

     

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  • Complex Numbers and Quadratic Equations Assignments 8

    Find the modulus and argument of the complex number.

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  • Complex Numbers and Quadratic Equations Assignments 9

    Let . Find

    (i) , (ii) 

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  • Complex Numbers and Quadratic Equations Assignments 10

    If a + ib =, prove that a2 + b2 = 

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  • Complex Numbers and Quadratic Equations Assignments 11

    If  find.

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  • Complex Numbers and Quadratic Equations Assignments 12

    Solve the equation 21x2 - 28x + 10 = 0

     

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  • Complex Numbers and Quadratic Equations Assignments 13

    Solve the equation 27x2 - 10x + 1 = 0

     

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  • Complex Numbers and Quadratic Equations Assignments 14

    Solve the equation

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  • Complex Numbers and Quadratic Equations Assignments 15

    Solve the equation

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  • Complex Numbers and Quadratic Equations Assignments 16

    Convert the following in the polar form:

    (i) , (ii) 

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  • Complex Numbers and Quadratic Equations Assignments 17

    If x - iy =prove that.

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  • Complex Numbers and Quadratic Equations Assignments 18

    Reduce to the standard form.

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  • Complex Numbers and Quadratic Equations Assignments 19

    For any two complex numbers z1 and z2, prove that

    Re (z1z2) = Re z1 Re z2 - Im z1 Im z2

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  • Complex Numbers and Quadratic Equations Assignments 20

    Evaluate: 

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  • Complex Numbers and Quadratic Equations Assignments 21

    Solve the equation 

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  • Complex Numbers and Quadratic Equations Assignments 22

    Solve the equation

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  • Complex Numbers and Quadratic Equations Assignments 23

    Solve the equation 

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  • Complex Numbers and Quadratic Equations Assignments 24

    Solve the equation 

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  • Complex Numbers and Quadratic Equations Assignments 25

    Solve the equation x2 + 3x + 5 = 0

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  • Complex Numbers and Quadratic Equations Assignments 26

    Solve the equation -x2 + x - 2 = 0

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  • Complex Numbers and Quadratic Equations Assignments 27

    Solve the equation x2 + 3x + 9 = 0

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  • Complex Numbers and Quadratic Equations Assignments 28

    Solve the equation 2x2 + x + 1 = 0

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  • Complex Numbers and Quadratic Equations Assignments 29

    Solve the equation x2 + 3 = 0

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  • Complex Numbers and Quadratic Equations Assignments 30

    Convert the given complex number in polar form: i

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  • Complex Numbers and Quadratic Equations Assignments 31

    Convert the given complex number in polar form: 

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  • Complex Numbers and Quadratic Equations Assignments 32

    Convert the given complex number in polar form: -3

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  • Complex Numbers and Quadratic Equations Assignments 33

    Convert the given complex number in polar form: - 1 - i

     

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  • Complex Numbers and Quadratic Equations Assignments 34

    Convert the given complex number in polar form: - 1 + i

     

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  • Complex Numbers and Quadratic Equations Assignments 35

    Convert the given complex number in polar form: 1 - i

     

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  • Complex Numbers and Quadratic Equations Assignments 36

    Find the modulus and the argument of the complex number

     

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  • Complex Numbers and Quadratic Equations Assignments 37

    Find the modulus and the argument of the complex number

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  • Complex Numbers and Quadratic Equations Assignments 38

      

    Express the following expression in the form of a + ib.

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  • Complex Numbers and Quadratic Equations Assignments 39

      

    Find the multiplicative inverse of the complex number -i

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  • Complex Numbers and Quadratic Equations Assignments 40

     

    Find the multiplicative inverse of the complex number 

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  • Complex Numbers and Quadratic Equations Assignments 41


    Find the multiplicative inverse of the complex number 4 - 3i

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  • Complex Numbers and Quadratic Equations Assignments 42

    Express the given complex number in the form a + ib:

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  • Complex Numbers and Quadratic Equations Assignments 43

     

    Express the given complex number in the form a + ib:

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  • Complex Numbers and Quadratic Equations Assignments 44

     Express the given complex number in the form a + ib:  (1 - i)4

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  • Complex Numbers and Quadratic Equations Assignments 45

    Express the given complex number in the form a + ib:

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  • Complex Numbers and Quadratic Equations Assignments 46

     

    Express the given complex number in the form a + ib:

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  • Complex Numbers and Quadratic Equations Assignments 47

     

    Express the given complex number in the form a + ib: (1 - i) - (-1 + i6)

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  • Complex Numbers and Quadratic Equations Assignments 48

     

     

    Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

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  • Complex Numbers and Quadratic Equations Assignments 49

     Express the given complex number in the form a + ib: i-39

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  • Complex Numbers and Quadratic Equations Assignments 50

     Express the given complex number in the form a + ib: i9 + i19

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  • Complex Numbers and Quadratic Equations Assignments 51

     Express the given complex number in the form a + ib:

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