HSN.CN.A.2 math practice. Learn by doing.

Expand: $(-1+5i)(2-3i)=-2+3i+10i-15i^{2}$. Since $i^{2}=-1$, this is $-2+13i+15=13+13i\textsf{.}$

$|6 + 8i| = \sqrt{6^2 + 8^2} = \sqrt{100} = 10$.

$\sqrt{49} = 7$ and $\sqrt{-4} = 2i$. So $\sqrt{49} + \sqrt{-4} = 7 + 2i$.

Expand: $(4+i)(3+2i)=12+8i+3i+2i^{2}$. Since $i^{2}=-1$, this is $12+11i-2=10+11i\textsf{.}$

$(3i)^{2} = 9i^{2} = 9(-1) = -9$.

$\sqrt{81} = 9$ and $\sqrt{-25} = 5i$. So $\sqrt{81} + \sqrt{-25} = 9 + 5i$.

Expand: $(1+6i)(1-6i)=1-6i+6i-36i^{2}=1-36i^{2}$. Since $i^{2}=-1$, this is $1+36=37\textsf{.}$

$i^{3} = i^{2} \cdot i = (-1)(i) = -i$.