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For two complex numbers z1&z2 (a z1+b ...

For two complex numbers `z_1&z_2` `(a z_1+b z_1)(c z_2+d z_2)=(c z_1+bz_2)if(a , b , c , d in R):`

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For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

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For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|

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Which of the following is correct for any tow complex numbers z_1a n dz_2? (a) |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.

Which of the following is correct for any tow complex numbers z_1a n dz_2? |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

For two unimodular complex number z_1a n dz_2 [[barz_1, -z_2], [barz_2, z_1]]^(-1) [[(z_1, z_2], [-barz_2, barz_1]]^(-1) is equal to [(z_1, z_2), (z_1bar, z_2bar)]^ b. [1 0 0 1] c. [1//2 0 0 1//2] d. none of these

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
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