SAT Mathematics Practice Test 6

For a complex number written in the form a + bi, a is called the real part of the complex number and b is called the imaginary part. The sum of two complex numbers, $\mathit{a}+\mathit{b}\mathit{i}$ and $\mathit{c}+\mathit{d}\mathit{i},$ is found by adding real parts and imaginary parts, respectively; that is, $\left(\mathit{a}+\mathit{b}\mathit{i}\right)+\left(\mathit{c}+\mathit{d}\mathit{i}\right)=\left(\mathit{a}+\mathit{c}\right)+\left(\mathit{b}+\mathit{d}\right)\mathit{i}.$ Therefore, the sum of $2+3\mathit{i}$ and $4+8\mathit{i}$ is $\left(2+4\right)+\left(3+8\right)\mathit{i}=6+11\mathit{i}$.
Choice A is incorrect and is the result of disregarding i and adding all parts of the two complex numbers together, $2+3+4+8=17.$ Choice B is incorrect and is the result of adding all parts ofthe two complex numbers together and multiplying the sum by i. Choice D is incorrect and is the result of multiplying the real parts and imaginary parts of the two complex numbers, $\left(2\right)\left(4\right)=8\mathit{a}\mathit{n}\mathit{d}(3\left(8\right)=24,$ instead of adding those parts together.