Related InterviewSolutions

• If `z` is a complex number and `z=bar(z)`, then prove that `z` is a purely real number.A. `Re(z)=0`B. `Im(z)=0`C. `Re(z)=Im(z)`D. None of these
• both roots of the equation `(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0` areA. positiveB. negativeC. realD. None of these
• Find the complex number z satisfying the equations `|(z-12)/(z-8i)|=5/3,|(z-4)/(z-8)|=1`A. `6+ 3i`B. `6+8i, 6+17i`C. `6+8i , 6+4i`D. `6+17i`
• The roots of the equation `x^(2) +6ix-9=0` are :A. `pmi`B. `pm2i`C. `pm3i`D. None of these
• If `alpha!= beta` but `alpha^2 = 5alpha-3, beta^2 = 5beta - 3`, then find the equation whose roots are `alpha/beta and beta/alpha`.A. `3x^(2)-19x-3=0`B. `3x^(2)-19x+3=0`C. `3x^(2)+19x+3=0`D. None of these
• The conjugate of the complex number `(a+ib)` is :A. `-a-ib`B. `-a+ib`C. `a-ib`D. None of these
• If `(3+2isintheta)/(1- 2isintheta) ` is real , then general value of `theta` is :A. ` (npi)/(2),nin1`B. ` npi,nin1`C. `(npi)/(3),nin1`D. None of these
• If `arg((z-1)/(z+1))=pi/2` then the locus of z isA. parabolaB. circleC. pair of two straight linesD. None of the above
• Write the least positive integral value of `n`for which `((1+i)/(1-i))^n`is real.
• Show that a real value of `x`will satisfy hte equation `(1-i x)//(1+i x)=a-i b`if `a^2+b^2=1,w h e r ea ,b`real.A. 1B. 0C. -1D. None of these