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, $a+bi$ and $c+di,$ is found by adding real parts and imaginary parts, respectively; that is, $(a+bi)+(c+di)=(a+c)+(b+d)i.$ Therefore, the sum of $2+3i$ and $4+8i$ is $(2+4)+(3+8)i=6+11i$.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, $(2)(4)=8 \text{ and } (3(8)=24,$ instead of adding those parts together.