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z equals quantity negative 12 minus 3 times I end quantity over quantity 4 plus 7 times i end quantity comma

User Xevincent
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1 Answer

3 votes

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

User Rishabh Kumar
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