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If z=2-3i, express (1-2z)/(z-3) in the f...

If z=2-3i, express `(1-2z)/(z-3)` in the form A+iB where A and B are real.

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The correct Answer is:
`-(3)/(2)+i(-(3)/(2))`
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CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(SHORT ANSWER TYPE QUESTION )
  1. If z(1)=4-3iand z(2)=-12+5i, "show that", |z(1)z(2)|=|z(1)||z(2)|

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  2. If z(1)=4-3iand z(2)=-12+5i, "show that", |z(1)/z(2)|=|z(1)|/|z(2)|

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  3. If z=2-3i, express (1-2z)/(z-3) in the form A+iB where A and B are rea...

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  4. If (2+i)/(2-3i)=A+iB (A,B" ""are real", i =sqrt(-1)), find the value o...

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  5. If (2+i)/(2-3i)=A+iB (A,B" ""are real", i =sqrt(-1)), find the value o...

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  6. Express each of the following complex numbers in modulus-amlitude form...

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  7. Express each of the following complex numbers in modulus-amlitude form...

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  8. Express each of the following complex numbers in modulus-amlitude form...

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  9. Express each of the following complex numbers in modulus-amlitude form...

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  10. Express each of the following complex numbers in modulus-amlitude form...

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  11. If a,b,c,d,x,y are real and (a+ib)(c+id)=x+iy, show that , (a-ib)(c-id...

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  12. If a,b,c,d,x,y are real and (a+ib)(c+id)=x+iy, show that , (ac-bd)^(2)...

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  13. If (a+ib)/(c+id)=x+iy prove that, (a-ib)/(c-id)=x-iy

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  14. If (a+ib)/(c+id)=x+iy prove that, (a^(2)+b^(2))/(c^(2)+d^(2))=x^(2)+y^...

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  15. If x+iy=sqrt((a+ib)/(c+id))" ""prove that", (x^(2)+y^(2))^(2)=(a^(2)+...

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  16. If a,b,p,q are real and 3sqrt(a-ib)=p-iq" ""prove that" " " 3sqrt(a+ib...

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  17. If z=x+iy and |z+6|=|2z+3|, porve that x^(2)+y^(2)=9.

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  18. If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

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  19. If z=x+iyand |2z+1|=|z-2i|, "prove that" " " 3(x^(2)+y^(2))+4(x+y)=3 [...

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  20. If x=2+3i and y=2-3i then find the values of (x^(3)-y^(3))/(x^(3)+y^(...

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