Question

Simplify the given expression:

4/3-2i

Answer 1

The answer is
`(12+8i)/(13)`


`(4)/(3-2i) = (4(3+2i))/((3-2i)(3+2i)) \\ \\ (a-b)(a+b) = a^(2) -b^(2) \\ \\ (4(3+2i))/((3-2i)(3+2i)) = (4*3+4*2i)/(3 ^(2)- (2i)^(2) )= (12+8i)/(9- (2)^(2)(i)^(2) )= (12+8i)/(9-4(i)^(2)) \\ \\ (i)^(2) = -1 \\ \\ (12+8i)/(9-4(i)^(2))== (12+8i)/(9-4*(-1))}= (12+8i)/(9+4) = (12+8i)/(13)`