c Apply the Distributive Property. Recall that i^2=- 1.
A
a See solution.
B
b See solution.
C
c See solution.
Practice makes perfect
a We can show that the given equation is true by considering its left-hand side. Then, we will simplify the expression on the left-hand side and show that it is equal to the expression on right-hand side.
(i-3)^2 = 8-6iTo simplify the expression on the left-hand side, let's start by applying the formula, (a-b)^2=a^2-2ab+b^2. Recall the definition of the imaginary unit, i^2=- 1.
Finally, note that the obtained expression is equal to the expression on the right-hand side of the given equation.
8-6i = 8-6i
Therefore, the given equation is true.
b Similarly as in Part A, we can show that the given equation is true by considering the left-hand side. Then, we will simplify the expression on the left-hand side and show that it is equal to the expression on right-hand side.
(2i-1)(3i+1) = -7-iTo simplify the expression on the left-hand side, let's start by applying the Distributive Property. Recall the definition of the imaginary unit i, i^2=- 1.
Finally, note that the obtained expression is equal to the expression on the right-hand side of the given equation.
-7-i = -7-i
Therefore, the given equation is true.
c We can show that the given equation is true by considering the left-hand side. Then, we will simplify the expression on the left-hand side and show that it is equal to the expression on right-hand side.
(3-2i)(2i+3) = 13To simplify the expression on the left-hand side, let's start by applying the Distributive Property. Recall the definition of the imaginary unit i, i^2=- 1.
Finally, note that the obtained expression is equal to the expression on the right-hand side of the given equation.
13 = 13
Therefore, the given equation is true.
