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If a rg(z1)=170^0a n d arg(z2)70^0 , the...

If `a rg(z_1)=170^0a n d arg(z_2)70^0` , then find the principal argument of `z_1z_2dot`

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To find the principal argument of the product of two complex numbers \( z_1 \) and \( z_2 \), given their arguments, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Arguments**: - We are given that \( \text{arg}(z_1) = 170^\circ \) and \( \text{arg}(z_2) = 70^\circ \). 2. **Use the Property of Arguments**: ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

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  17. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)+.......

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  18. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the val...

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  19. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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  20. Given that |z1+z2|^2=|z1|^2+|z2|^2, prove that z1/z2 is purely imagina...

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