Question

1)Calcule os seguintes produtos:

   
  a) (2 + 3i) (3 - 2i)                                                    
                b) (1 + 3i) (1 + i)

 
                                                                              

Answer 1

a)

$(2+3i)(3-2i)=2\cdot3-2\cdot2i+3i\cdot3-3i\cdot2i\\(2+3i)(3-2i)=6-4i+9i-6i^{2}\\(2+3i)(3-2i)=6+5i-6(-1)\\(2+3i)(3-2i)=6+5i+6\\(2+3i)(3-2i)=12+5i$

b)

$(1+3i)(1+i)=1\cdot1+1\cdot i+3i\cdot1+3i\cdot i\\(1+3i)(1+i)=1+i+3i+3i^{2}\\(1+3i)(1+i)=1+4i+3(-1)\\(1+3i)(1+i)=1+4i-3\\(1+3i)(1+i)=-2+4i$