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Prove that abs(costheta-isintheta) = 1...

Prove that `abs(costheta-isintheta) = 1`

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Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

Prove that (costheta)/(1+sintheta)=tan((pi)/(4)-(theta)/(2))

Prove that (1+sintheta-cos theta)/(1+sin theta+costheta)=tantheta//2

Show that tan^-1(costheta/(1+sintheta)) is independent of trigonometric functions.

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

The parametric representation of a point on the ellipse whose foci are (3,0) and (-1,0) and eccentricity 2//3 , is a) (1+3costheta,sqrt(3)sintheta) b) (1+3costheta,5sintheta) c) (1+3costheta,1+sqrt(5)sintheta) d) (1+3costheta,sqrt(5)sintheta)

Given x^2=cos2theta Show that tan^-1((costheta+sintheta)/(costheta-sintheta))=pi/4+theta

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) deduce the value of tan(22 1/2)^@

Solve costheta+cos3theta-2cos2theta=0 .

A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Prove that abs((1+i)/(1-i)) = 1

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  2. If a+ib = sqrt((1+i)/(1-i)), prove that a^2+b^2=1

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  3. Prove that abs(costheta-isintheta) = 1

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  4. If (costheta-isintheta)^2 = x -iy, show that x^2+y^2 = 1

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  5. Complete the following table

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  6. When two complex numbers are equal? Find the real values of x and y fo...

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  7. Match the following

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  8. Fill in the blanks by choosing the correct answer from the bracket ove...

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  9. Suppose z1 = 1 - i and z2 = -2 + 4i Find z1z2

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  10. Suppose z1 = 1 - i and z2 = -2 + 4i Find overlinez1

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  11. Suppose z1 = 1 - i and z2 = -2 + 4i Find Im ((z1z2)/z1) and Re ((z1z2...

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  12. Suppose z1 = 1 - i and z2 = -2 + 4i Joseph evaluted abs((z1z2)/z1) usi...

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  13. Suppose z = x + iy and w = (1-iz)/(z-i) Find 1 - iz and z - 1 in the s...

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  14. Suppose z = x + iy and w = (1-iz)/(z-i) Find absw. If absw = 1, prove...

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  15. Consider the complex number z1 = 2 - i and z2 = -2 + i Find (z1z2)/z1...

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  16. Consider the complex number z1 = 2 - i and z1 = -2 + i Raju prove tha...

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  17. Consider the complex number z1 = 2 - i and z2 = 2 + i Find 1/(z1z2). ...

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  18. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  19. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  20. Represent the following complex numbers as points in the argand plane ...

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