review the graphs of complex numbers z and w.\nwhat is $\frac{z}{w}$?\n$\boldsymbol{-4 + 16i}$\n$\boldsymbol{…

Explanation:

Step1: Identify complex numbers

From the graph: $z = 6 + 10i$, $w = 1 + i$

Step2: Multiply by conjugate of $w$

Multiply numerator and denominator by $1-i$: $\frac{z}{w} = \frac{(6+10i)(1-i)}{(1+i)(1-i)}$

Step3: Expand numerator

Use FOIL method: $(6+10i)(1-i) = 6(1) + 6(-i) + 10i(1) + 10i(-i) = 6 -6i +10i -10i^2$ Since $i^2=-1$, this becomes $6 +4i +10 = 16 +4i$

Step4: Expand denominator

Difference of squares: $(1+i)(1-i) = 1^2 - i^2 = 1 - (-1) = 2$

Step5: Simplify the fraction

Divide numerator by denominator: $\frac{16+4i}{2} = 8 + 2i$

Answer:

8 + 2i