Which term of the sequence `12+8i ,\ 11+6i ,\ 10+4i ,...` is (a) purely real and (b). purely imaginary?

Which term of the sequence 8-6i ,7-4i ,6-2i ,..... is (i) purely real (ii) purely imaginary?

Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pure real number ? (b) pure imaginary number ?

Find the 24th term of the sequence: 12,10,8,6…..

If a and b are complex and one of the roots of the equation x^(2) + ax + b =0 is purely real whereas the other is purely imaginary, then

If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) purely real (b)purely imaginary (c)an imaginary number that is not purely imaginary,a+i b , w h e r ea!=0,b!=0 (d)both purely real and purely imaginary

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real roots

Which term of the progression 18 ,-12 ,8, i s(512)/(729)?

If a ,b are complex numbers and one of the roots of the equation x^2+a x+b=0 is purely real, whereas the other is purely imaginary, prove that a^2- (bar a)^2=4b .

Find the real number x if (x−2i)(1+i) is purely imaginary.

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary