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Find the Area bounded by complex numbers `arg|z|lepi/4` and `|z-1|lt|z-3|`

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To find the area bounded by the complex numbers defined by the conditions \( \arg(z) \leq \frac{\pi}{4} \) and \( |z - 1| < |z - 3| \), we can follow these steps: ### Step 1: Understand the first condition \( \arg(z) \leq \frac{\pi}{4} \) The condition \( \arg(z) \leq \frac{\pi}{4} \) represents the region in the complex plane where the angle (argument) of the complex number \( z \) is less than or equal to \( \frac{\pi}{4} \). This corresponds to the area below the line \( y = x \) in the first quadrant. ### Step 2: Understand the second condition \( |z - 1| < |z - 3| \) ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. Solve the equation |z|=z+1+2idot

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  2. Find the range of real number alpha for which the equation z+alpha|z-1...

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  3. Find the Area bounded by complex numbers arg|z|lepi/4 and |z-1|lt|z-3|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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