MCQ - 21-8753

Correct Answer: B

Explanation:

This question tests ones ability to recognize that when adding and subtracting complex numbers, the imaginary portions act like a variable during algebraic operations. When adding or subtracting complex numbers recall that it is the combination of like terms. The liked terms of complex numbers include the real portion of the complex number (the ${\displaystyle a}$'s), and the imaginary portion (the ${\displaystyle b}$'s) given the expression,

${\displaystyle (a+bi)\pm <!--\; \pm \; -->(a_1+b_{1}i)}$

For the purpose of Common Core Standards, "use the relation${\displaystyle i^2=-<!--\; -\; -->1}$, and the commutative, associate, and distributive properties to add, subtract, and multiply complex numbers", falls within the Cluster A of "perform arithmetic operations with complex numbers" (CCSS.MATH.CONTENT.HSF.CN.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Distribute the negative to each term within the second set of parentheses.

${\displaystyle (7+2i)-<!--\; -\; -->(6-<!--\; -\; -->4i)}$

${\displaystyle 7+2i-<!--\; -\; -->6-<!--\; -\; -->(-<!--\; -\; -->4i)}$

Recall that subtracting a negative number means adding a positive.

${\displaystyle 7+2i-<!--\; -\; -->6+4i}$

Step 2: Identify like terms.

Real portion: 7−6=1

Imaginary portion: ${\displaystyle 2i+4i=6i}$

Note: treat i as a variable.

Step 3: Combine like terms into one expression.

${\displaystyle 1+6i}$