Please I need help and I’m stumped here.

Step-by-step explanation:

1) For complex numbers addition, add the real parts and imaginary party separately.

(2 +5i) - (-6 + 3i) = 2 + 5i + 6 - 3i

                          = 2+ 6 + 5i - 3i

                          = 8 + 2i

2)Use FOIL method

(-4 +2i)(3 - 7i) = -4*3 + (-4)*(-7i) + 2i* 3  + (2i)*(-7i)

                    = -12 + 28i + 6i -14i²                 {i² = -1}

                   = -12 + 28i + 6i - 14*(-1)

                   = -12 + 28i + 6i + 14             {Combine like terms}

                 = -12 + 14 + 28i + 6i

                 = - 2 + 34i

3)Hint:

4)

5) 4x² + 28x + 49 = 4x² + 14x +14x + 7*7

                            = 2x(2x + 7) + 7(2x + 7)

                            =(2x+ 7)(2x + 7)

6) 2x² + 3x - 20 =  2x² +8x - 5x - 5 *4

                         =2x(x + 4) - 5(x + 4)

                       = (x + 4)(2x - 5)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4