Question

Write the expression as a complex number in standard form- -2i(1+i)(2+3i)

Answer 1

`\text{Standard form:}\ a+bi,\ a,b\in\mathbb{R}\\\\-2i(1+i)(2+3i)\qquad\text{use distributive property}\\\\=[(-2i)(1)+(-2i)(i)](2+3i)\\\\=(-2i-2i^2)(2+3i)\qquad i=√(-1)\to i^2=-1\\\\=(-2i+2)(2+3i)\qquad\text{use distributive property}\\\\=(-2i)(2)+(-2i)(3i)+(2)(2)+(2)(3i)\\\\=-4i-6i^2+4+6i\qquad i=√(-1)\to i^2=-1\\\\=-4i+6+4+6i\qquad\text{use commutative and associative property}\\\\=(6+4)+(-4i+6i)\\\\=\boxed{10+2i}`