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If the complex number z=x+i y satisfies...

If the complex number `z=x+i y` satisfies the condition `|z+1|=1,` then `z` lies on (a)x axis (b) circle with centre`(-1,0)` and radius`1` (c)y-axis (d) none of these

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`abs(z+1)=1`

`rArr abs(z+1)^2=1^2`

`rArr (z+1)(z+1)=1` ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If z and w are two complex number such that |zw|=1 and arg (z) – arg (...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the value of 1+i^(2)+i^(4)+i^(6)+...+i^(2n),

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

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  16. Prove that the following complex numbers are purely real: (i)((2+3i)/...

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

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  18. Find the values of following expressions: i^(49)+i^(68)+i^(89)+i^(110)...

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

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