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If for complex numbers z1 and z2 ,arg(z1...

If for complex numbers `z_1` and `z_2` ,`arg(z_1) - arg(z_2)=0` , then show that `|z_1-z_2| = | |z_1|-|z_2| |`

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We have, `z_1`and `z_2`​ complex number such that,
Let, `z_1​=∣z_1​∣(costheta_1​+isintheta_1​)`
And `z_2​=∣z_2​∣(costheta_2​+isintheta_2​)`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If arg(z-1)=arg(z+3i), then find (x-1):y, where z=x+iy

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  2. Solve the equation |z|=z+1+2idot

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  3. If for complex numbers z1 and z2 ,arg(z1) - arg(z2)=0 , then show tha...

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  4. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  5. If (1+i)z=(1-i) z , then show that z=-i z dot

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  6. Write the conjugate of (2-i)/((1-2i)^2) .

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  7. lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imagina...

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  8. If z and w are two complex number such that |zw|=1 and arg (z) – arg (...

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  9. The value of (1+i)^4+(1-i)^4 is

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  10. If the complex number z=x+i y satisfies the condition |z+1|=1, then ...

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  11. If z = x + iy lies in III quadrant, then bar z / z also lies in III qu...

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

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  13. Let z1=r1(costheta1+isintheta1) and z2=r2(costheta2+isintheta2) be t...

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

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

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

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

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

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

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

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