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Show that the complex number ((4+3i)/(3...

Show that the complex number ` ((4+3i)/(3 + 4i)) ((4 -3i)/(3-4i))` is purely real.

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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Try Yourself
  1. Express 1/(1+cos theta-i sin theta) in the form of a +ib.

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  2. Express (1 /(2 -2i)+3/(1+i)) ((3+ 4i)/(2-4i)) in the form of a +ib

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  3. Show that the complex number ((4+3i)/(3 + 4i)) ((4 -3i)/(3-4i)) is pu...

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  4. Find real q such that (3+2isintheta)/(1-2isintheta) is purely real.

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  5. Plot the conjegate of the complex number 2-3i on the Argand plane.

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  6. Plot the conjegate of the complex number -7-4i on the Argand plane. ]

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  7. Mutiply ( 5 +2i) by its conjugate.

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  8. Find the conjugate of ((1-2i)^(2))/(2 + i)

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  9. if z = 2 + i + 4i^(2) -6i^(3) then verify that (i) (bar(z^(2)) = (...

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  10. if z=3 -2i, then verify that (i) z + barz = 2Rez (ii) z - bar...

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  11. if z(1) = 3-i and z(2) = -3 +i, then find Re ((z(1)z(2))/(barz(1))...

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  12. if z(1)=2-i, and z(2) = 1+ i, then find Im(1/(z(1)z(2)))

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  13. Find real values of x and y for which the complex numbers 7 + ix^(2)y...

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  14. Find real number x and y if (x-iy)(4 + 7i) is the conjugate of 29-2i.

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  15. find the conjugate of (sqrt2 -isqrt2)/(2sqrt5-isqrt2)

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  16. If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)...

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  17. Represent the modulus of 3+4i in the Argand plane.

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  18. Represent the modulus of 1+I, in the Argand plane.

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  19. Find the modulus of (2 -3i)/( 4+i)

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  20. Find the modulus of ((3+2i)^(2))/(4-3i)

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