SAT Math Multiple Choice Question 613: Answer and Explanation

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Test Information

Question: 613

13. If the complex number A satisfies the equation A(2 - i) = 2 + i, where Images, what is the value of A?

  • A. 5 - i
  • B. 5 + i
  • C. Images
  • D. Images

Correct Answer: C

Explanation:

C

Special Topics (complex numbers) HARD

A(2 - i) = 2 + i

Divide by (2 - i):

Images

Multiply numerator and denominator by the conjugate (2 + i):

Images

FOIL:

Images

Combine terms:

Images

Substitute i2 = - 1:

Images

Simplify:

Images

Combine terms:

Images

Distribute to express in standard a + bi form:

Images

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