The answer is A. 11/10 + 13/10 i.
Recognize the goal: We need to express z in standard form, which means writing it as a + bi, where a and b are real numbers.
Simplify the expression:
Start by multiplying both the numerator and denominator of the given expression by the denominator's complex conjugate, which is 4 + 2i.
This eliminates the imaginary unit (i) in the denominator:
z = (7 + 3i) * (4 + 2i) / (4 - 2i) * (4 + 2i)
= (28 + 14i + 12i + 6i^2) / (16 + 4)
= (28 + 26i - 6) / 20
= (22 + 26i) / 20
= 11/10 + 13/10 i
Identify the standard form: The final expression, 11/10 + 13/10 i, is now in standard form with a = 11/10 and b = 13/10.
Complete Question:
Given z equals quantity 7 plus 3 times I end quantity over quantity 4 minus 2 times I end quantity comma what is z in standard form?
a. 11/10 + 13/10 i
b. - 17/6 - 13/3 i
c. - 11/10 - 13/10 i
d. 17/6 + 13/3 i