Find the real value of a for which `3i^3-2a i^2+(1-a)i+5` is real.

Find the real value of a for which 3i^(3)-2ai^(2)+(1-a)i+5 is real

6/ Find the real value of ? for which 1+cos?1-2i cos ? is purely real.

Find real value of theta for which (3+2i sin theta)/(1-2i sin theta) is purely real.

Find real value of theta for which (3+2i sin theta)/(1-2i sin theta) is purely real.

Find the real values of x and y for which (1+i)y^2+(6+i)=(2+i)x

Find real values of theta for which (4 + 3i sin theta) / (1 - 2i sin theta) is purely real.

Find the real values of x and y for which the following equation is satisfied: ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i

Find the smallest positive integer value of n for which ((1+i)^n)/((1-i)^(n-2)) is a real number.

Find the real values of x and y for which (1+i)y^(2)+(6+i)=(2+i)x

Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i