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Write the value of sqrt(-25)xxsqrt(-9)do...

Write the value of `sqrt(-25)xxsqrt(-9)dot`

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To solve the expression \( \sqrt{-25} \times \sqrt{-9} \), we will follow these steps: ### Step 1: Rewrite the square roots of negative numbers We know that \( \sqrt{-a} = i \sqrt{a} \), where \( i \) is the imaginary unit defined as \( i = \sqrt{-1} \). So, we can rewrite: \[ \sqrt{-25} = \sqrt{-1 \times 25} = \sqrt{-1} \times \sqrt{25} = i \times 5 = 5i ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the principal argument of (1+isqrt(3))^2dot

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  2. Find z ,\ if\ |z|=4\ and \ arg(z)=(5pi)/6 .

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  3. Write the value of sqrt(-25)xxsqrt(-9)dot

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

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  5. If |z+4|lt=3 then find the greatest and least values of |z+1|dot

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  6. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

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  7. If n in NN ,then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3).

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  8. Find the real value of a for which 3i^3-2a i^2+(1-a)i+5 is real.

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  9. If |z|=2 and arg (z)=pi/4 , find z.

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  10. Write the argument of (1+isqrt(3))(1+i)(costheta+isintheta).

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  11. The value of (1+i)(1+i^2)(1+i^3)(1+i^4) is a. 2 b. 0 c. 1 d. i

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  12. If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2...

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  13. If sqrt(a+i b)=x+i y ,\ then possible value of sqrt(a-i b) is a. x^...

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  14. If z=cos(pi/4)+isin(pi/6) , then a. |z|=1, arg(z)=\ pi/4 b. |z|=1, a...

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  15. The polar form of (i^(25))^3 is

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  16. If i^2=-1, then the sum i+i^2+i^3+... upto 1000 terms is equal to a....

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  17. If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/...

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  18. If a=costheta+isintheta, then (1+a)/(1-a) is a. cot(theta/2) b. cot...

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  19. If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then 2. 5. 10. 17... (1+n^2\ )...

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  20. If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/...

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