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Convert the complex number z=(i-1)/(cosp...

Convert the complex number `z=(i-1)/(cospi/3+isinpi/3)`in the polar form.

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To convert the complex number \( z = \frac{i - 1}{\cos \frac{\pi}{3} + i \sin \frac{\pi}{3}} \) into polar form, we will follow these steps: ### Step 1: Simplify the denominator First, we need to evaluate \( \cos \frac{\pi}{3} \) and \( \sin \frac{\pi}{3} \): \[ \cos \frac{\pi}{3} = \frac{1}{2}, \quad \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} \] Thus, we can rewrite the denominator: ...
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NCERT ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the modulus and the arguments of the complex number z = - 1 - is...

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  2. Find the modulus and the arguments of the complex number z=-sqrt(3)+i

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  3. Convert the complex number z=(i-1)/(cospi/3+isinpi/3)in the polar form...

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  4. Find real theta such that (3+2isintheta)/(1-2isintheta)is purely real...

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

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  6. Find the modulus and argument of the complex numbers : (i) (1+i)/(1-i...

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  7. Find the conjugate of ((3-2i)(2+3i))/((1+2i)(2-i)).

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  8. Solve: sqrt(5)x^(2) + x + sqrt(5) = 0

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  9. Solve x^2+x+1=0.

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  10. Convert of the complex number in the polar form: -1 + i

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  11. Express of the complex number in the form a + i b. (-2-1/3i)^3

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  12. Find the multiplicative inverse of the complex number. 4 - 3i

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  13. Find the multiplicative inverse of the complex number. sqrt(5)+3i

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  14. Find the multiplicative inverse of the complex number. i

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  15. Express the following expression in the form of a + i b((3+isqrt(5))(3...

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  16. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

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  17. Solve the equation:x^2+x+1/(sqrt(2))= 0

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  18. Solve the equation:sqrt(3)x^2-sqrt(2)x+3sqrt(3)= 0

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  19. Convert of the complex number in the polar form: - 3

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  20. Solve the equation -x^2+x-2=0

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