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Let z1=r1(costheta1+isintheta1)a n dz2=r...

Let `z_1=r_1(costheta_1+isintheta_1)a n dz_2=r_2(costheta_2+isintheta_2)` be two complex numbers. Then prove that `|z_1+z_2|^2=r1 2+r2 2+2r_1r_2cos(theta_1-theta_2)` or `|z_1+z_2|^2=|z_1|^2+|z_2|^2+2|z_1||z_2|^()_cos(theta_1-theta_2)`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If z = x + iy lies in III quadrant, then bar z / z also lies in III qu...

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  2. If a=costheta+i sintheta, find the value of (1+a)/(1-a)dot

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  3. Let z1=r1(costheta1+isintheta1)a n dz2=r2(costheta2+isintheta2) be two...

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  4. For a positive integer n , find the value of (1-i)^n(1-1/i)^ndot

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  5. If (1+i)(1+2i)(1+3i)........(1+n i)=a+i b ,t h e n2xx5xx10 ....(1+n^2)...

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  6. Perform the indicated operation and find the result in the form a+i bd...

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  7. Let z1=2-i ,""""z2=-2+i . Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1...

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  8. Which of the following is correct for any tow complex numbers z1a n dz...

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  9. If z1a n dz2 are two complex numbers such that |z1|=|z2|a n d arg(z1)...

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  10. Evaluate sum(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

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  11. Evaluate 1+i^2+i^4+i^6+...+i^(2n)dot

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  12. Show that: {i^(19)+(1/i)^(25)}^2=-4 (ii) {i^(17)-(1/i)^(34)}^2=2i (ii...

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  13. If z1, z2 in C , then say which are true and false - ...

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  14. Prove that the following complex number is purely real: (i)((2+3i)/(3+...

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  15. Show that 1+i^(10)+i^(20)+i^(30) is a real number.

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  16. Find the values of following expression:1+i^2+i^4+i^6+i^8+doti^(20)

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  17. If (a+i b)(c+i d)(e+if)(g+i h)=A+i B prove that (a^2+b^2)(c^2+d^2)(e...

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  18. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

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  19. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

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  20. If z is a complex number such that |z|=1, prove that (z-1)/(z+1) is pu...

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