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Complex Numbers and Quadratic Equations

Short Answer Type

71.

Find the modulus of the following complex numbers :

$space space space space fraction numerator 3 minus 4 straight i over denominator 4 minus 3 straight i end fraction$

107 Views

72.

Find the modulus of the following complex numbers :

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111 Views

73.
Solve x²+ 3 = 0

Given x² + 3 = 0

or x²= -3

or $space space space space space straight x space equals space plus-or-minus square root of negative 3 end root space space equals space plus-or-minus square root of 3 space straight i$

127 Views

74.

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135 Views

75.

Conver $straight pi over 12$ to degrees.

115 Views

76.

Write the complex number $space space space space space space space space fraction numerator straight i minus 1 over denominator cos begin display style straight pi over 3 end style plus space straight i space sin begin display style straight pi over 3 end style end fraction$ in the polar form.

119 Views

77.

Write the conjugate of z = – 3 – 21

129 Views

78.

Find the value of the following : $space space space space open parentheses 1 plus straight i close parentheses to the power of 4 open parentheses 1 plus 1 over straight i close parentheses to the power of 4$

133 Views

Multiple Choice Questions

79.

The sum of all real values of x satisfying the equation
$left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent$ is:

3
-4
6
6

654 Views

80.

A complex number z is said to be unimodular, if |z|= 1. suppose z₁ and z₂ are complex numbers such that $fraction numerator straight z subscript 1 minus 2 straight z subscript 2 over denominator 2 minus straight z subscript 1 begin display style stack straight z subscript 2 with minus on top end style end fraction$ is unimodular and z₂ is not unimodular. Then, the point z₁ lies on a