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Convert the following in the polar form ...

Convert the following in the polar form : (i) `(1+7i)/((2-i)^2)` (ii) `(1+3i)/(1-2i)`

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NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) ...

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  2. Convert the following in the polar form : (i) (1+7i)/((2-i)^2) (ii) (...

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  3. Perform the indicated operation and find the result in the form a+i b ...

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  4. Prove that ((-1+isqrt(3))/(2))^(3) is a positive integer.

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  5. Convert [(3+2i)/( 3-2i)+ (3 -2i)/(3+2i)] in the form of (a+ib).

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  6. Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqr...

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  7. Find the sum and product of the complex number (3-4i) with its conjug...

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  8. Find the sum and product of the complex number (-1 +2i) with its conj...

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  9. Find the multiplicative inverse of the following complex number: (2+sq...

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  10. Write the following in the form of ordered pair : (i) 3-2i (ii)...

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  11. Convert the following in the form of a complex number : (i) (2, -5)...

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  12. Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+...

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  13. If z=1+2i, show that z^(2)-2z+5=0. Hence find the value of z^(3) +7z^...

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  14. Z=-5+4i then Z^4 +9Z^3 +35Z^2 – Z + 4 =

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  15. If z(1)=2-i, z(2)=1+ 2i, then find the value of the following : (i)...

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  16. If x + i y =(a+i b)/(a-i b),prove that x^2+y^2=1.

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  17. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

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  18. If ((a^(2)+1)^(2))/(2a-i) = a + iy , then what is the value of x^...

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

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  20. The complex number z is purely imaginary , if

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