`(3 + 2i)^(3) = ?`

Express (2 + 3i)^(3) in the form (a + ib).

Prove that the complex number ((3+2i)/(2-3i)) + ((3-2i)/(2+ 3i)) is purely real.

Express (2-3i)^(3) in the form (a + ib).

Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) (-3+(1)/(2)i)^(3) (iii) (1-i)(3+4i) (iv) (1+i)(1+ 2i)(1+ 3i) (v) (3+5i)/(6-i) (vi) ((2+3i)^(2))/(2+i) (vii) ((1+ i)(2+i))/((3+i)) (viii) (2-i)^(-3)

(3+5i)/(2-3i)

Reduce ((1)/(1+2i)+(3)/(1-i))((3-2i)/(1+3i)) to the form (a + ib).