rarr sqrt(((2+3i)/(3-2i))^(2)+((2*3i)/(3+2i))^(2))

Show that ((sqrt(3))/(2) + (i)/(2))^(5) + ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)

Prove that the following complex numbers are purely real: (i) ((2+3i)/(3+4i))((2-3i)/(3-4i)) (ii) ((3+2i)/(2-3i))((3-2i)/(2+3i))

sqrt(3)+(sqrt(3)-i2)-(3-i2)

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

Find the principal argument of the complex (1+i)^(5)(1+sqrt(3i))^(2) number ((1+i)^(5)(1+sqrt(3i))^(2))/(-2i(-sqrt(3)+i))

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

Verify that bar((2+3i)(1-2i)) = bar((2+3i)) bar( (1-2i))

If z = ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)) , then |z| is equal to

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (2-3i)/(4-i) (ii) (2+3i)/(-5-4i) (iii) (1+i)/(3+i) (iv) (3+2i)/(4-3i)