Step-by-step explanation:
Let the complex numbers be [tex]a+ib\textrm{ and }c+id[/tex].
Given, sum is [tex]10i[/tex], difference is [tex]-4[/tex] and product is [tex]-29[/tex].
[tex](a+c)+i(b+d)=10i[/tex] ⇒ [tex]a+c=0,b+d=10[/tex]
[tex](a-c)+i(b-d)=-4[/tex] ⇒ [tex]a-c=-4,b-d=0[/tex]
[tex]a=-2,c=2,b=5,d=5[/tex]
[tex](a+ib)(c+id)=(-2+5i)(2+5i)=-4-25=-29[/tex]
Hence, all three equations are consistent yielding the complex numbers [tex]-2+5i\textrm{ and }2+5i[/tex].
