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Show that e^(2m itheta)((icottheta+1)/(i...

Show that `e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.`

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To show that \[ e^{2m i \theta} \left( \frac{i \cot \theta + 1}{i \cot \theta - 1} \right)^m = 1, \] we will simplify the left-hand side step by step. ...
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Find the value of ((1-tantheta)/(1-cottheta))^2

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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. Find the Area bounded by complex numbers arg|z|lepi/4 and |z-1|lt|z-3|

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  2. Prove that traingle by complex numbers z(1),z(2) and z(3) is equilate...

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  3. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

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  4. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

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  5. Find the real part of (1-i)^(-i)dot

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  6. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

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  7. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

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  8. If a rg(z1)=170^0a n d arg(z2)70^0 , then find the principal argument ...

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  9. Find the value of expression (cos(pi/2)+isin(pi/2))(cos(pi/(2^2))+isin...

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  10. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

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  11. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

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  12. If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 z is purely real.

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  13. It is given the complex numbers z(1) and z(2), |z(1)| =2 and |z(2)| ...

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  14. Solve the equation z^(3) = barz (z ne 0)

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  15. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

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  16. Find the complex number satisfying the system of equations z^3+ omega^...

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  17. Express the following in a + ib form: (i) ((cos theta+ isin theta...

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  18. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

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  19. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

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  20. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

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