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In general, numbers are of two types imaginary number and a real number A real number can be studied easily but an imaginary number shows a different type of property which we will study in this topic by using iota.

probably option 3) 3

Option 1) Option 2) Option 3) Option 4)
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Principal value of argument                                                                                                                                        Hence, Principal value of argument=
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(given)  and  are of opposite sign So  will have a root in   Option (A)   f (α ) & f (β) are of opposite signs - Here, for one - wherein     Option 1) This is correct Option 2) This is incorrect Option 3) This is incorrect Option 4) This is incorrect
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We know,  Here,  It means maximum value of  is 4  Option (D)   Triangle Law of Inequality in Complex Numbers - - wherein |.| denotes modulus of complex number.     Option 1) This is incorrect Option 2) This is incorrect Option 3) This is incorrect Option 4) This is correct
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For   to have real and distinct roots   Quadratic Expression Graph when a> 0 & D > 0 - Real and distinct roots of & - wherein     Option 1) This is incorrect Option 2) This is correct Option 3) This is incorrect Option 4) This is incorrect
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b^2-4ac>0

then

it have

real and equal roots

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Coeff of  only required more is    Option (C)   Value of quadratic expression as negative. -  will be always negative, for all  , If   &     - wherein So, graph of    will be always below x-axis so   has no real roots.     Option 1) This is incorrect Option 2) This is incorrect Option 3) This is correct Option 4) This is incorrect
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