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if z = 2 + i + 4i^(2) -6i^(3) then veri...

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

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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Try Yourself
  1. Mutiply ( 5 +2i) by its conjugate.

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If z(1)=5+2i and z(2)=2 +i ,verify (i) |z(1)z(2)|= |z(1)||z(2)|

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  16. if z(1) =2+3i and z(2) = 1+i then find, |z(1)+z(2)|

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  17. Find the modulus and argument of -4i.

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  18. Find the modulus and argument of -3.

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  19. Convert the complex number (1+i)/(1-i) in the polar form

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  20. Convert the complex number 4/(1-isqrt3) in the polar form.

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