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Subject Test Math 1

Question 15 of 32

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SAT Subject Test

If a and b are real numbers, i to the power of 2 end exponent equals negative 1, and left parenthesis a plus b right parenthesis plus 5 i equals 9 plus a i, what is the value of b invisible times?

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4

Correct Answer: 
Yes

5

Correct Answer: 
No

9

Correct Answer: 
No

4 plus 5 i

Correct Answer: 
No

5 plus 4 i

Correct Answer: 
No

The correct answer is A.

To determine the value of b apply the fact that two complex numbers are equal if and only if the real and pure imaginary parts are equal. Since left parenthesis a plus b right parenthesis plus 5 i equals 9 plus a i, this gives the two equations a plus b equals 9 and 5 i equals a i, that is, a plus b equals 9 and 5 equals a. Therefore, 5 plus b equals 9, and b equals 4.

Question Difficulty: 
medium