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Show that the complex number `z ,` satisfying are `(z-1)/(z+1)=pi/4` lies on a circle.

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To show that the complex number \( z \) satisfying the equation \[ \frac{z-1}{z+1} = \frac{\pi}{4} \] lies on a circle, we can follow these steps: ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If |z-5i|=|z+5i , then the locus of zdot

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  2. If z1a n dz2 both satisfy z+\bar z =2|z-1| and a r g(z1-z2)=pi/4 , the...

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  3. Show that the complex number z , satisfying are (z-1)/(z+1)=pi/4 lies ...

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  4. If z=(1+7i)/((2-i)^2) , then (a)|z|=2 (b) |z|=1/2 c) a m p(z)=pi/4 (d)...

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  5. The value of (i^5+i^6+i^7+i^8+i^9)/(1+i) is (a) 1/2(1+i) (b) 1/2(1-...

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  6. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

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  7. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (a)(|z|)/2 ...

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  8. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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  9. What is the locus of z , if amplitude of (z-2-3i) is pi/4?

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  10. Write the sum of the series i+i^2+i^3+....... upto 1000 terms.

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  11. The sum and product of two complex numbers are real if and only if the...

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  12. If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)...

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  13. Write the value of a r g(z)+a r g(barz ) .

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  14. Find the conjugate of (1-i)/(1+i)

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  15. Find the conjugate of 1/(3+4i)dot

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  16. If (a+i b)/(c+i d)=x+i y , prove that (a-i b)/(c-i d)=x-i ya n d(a^2+b...

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  17. Find real values of xa n dy for which the complex numbers -3+i x^2ya n...

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  18. Find the real values of x and y for which (1+i)y^2+(6+i)=(2+i)x

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  19. Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i

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  20. If (x+i y)^(1//3)=a+i b ,x ,y ,a b in Rdot Show that x/a+y/b=4(a^2-b^...

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