(3+i)(3-i)(4+5i)

Question

i is an imaginary number

Answer 1

(3 + i)(3 - i)(4 + 5i)

Multiply out the brackets:

(3 + i)(3 - i)(4 + 5i)

= (3 + i)[3x4 + 3x(5i) - ix4 - ix(5i)]

And since,   i x i = - 1

So,

= (3 + i)[3x4 + 3x(5i) - ix4 - ix(5i)]

= (3 + i)[12 + 15i - 4i - (-5)]

= (3 + i)[12 + 5 + 11i]

= (3 + i)[17 + 11i]

= 3x17 + 3x(11i) + 17xi + ix(11i)

= 51 + 33i + 17i -11

= 40 + 50i