GMAT Math : DSQ: Graphing complex numbers

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Example Questions

Example Question #11 : Coordinate Geometry

Let and be real numbers.

From the number a + bi , subtract its complex conjugate. What is the result?

Statement 1: a+b= 10

Statement 2: a -b = 4

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

The complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)- (a - bi) = a -a +bi+bi = 2bi .

Therefore, it is necessary and sufficient to know in order to answer the question. Neither statement alone gives this information. However, the two statements together form a linear system that can be solved as follows:

a+b= 10

$- \underline{(a -b = 4)}$

We need go no further; since 2b=6 , the desired sum is (2b)i = 6i .

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Example Question #12 : Dsq: Graphing Complex Numbers

Let be a positive integer.

Evaluate $i^{N}$ .

Statement 1: is a multiple of 3.

Statement 2: is a multiple of 7.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume that both statements are true. The value of $i^{N}$ , a positive integer, is equal to $i^{R}$ , where is the remainder of the division of by 4, so we can use this fact to show that insufficient information is provided.

Case 1: N = 21 .

$21 \div 4 = 5\textup{ R }1$ , so

$i^{N} = i^{21} = i^{1}= i$

Case 2: N = 42 .

$42 \div 4 = 10 \textup{ R }2$ , so

$i^{N} = i^{42} = i^{2}= -1$

In both cases, both statements are true, but the value of $i^{N}$ differs.

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GMAT Math : DSQ: Graphing complex numbers

Study concepts, example questions & explanations for GMAT Math

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Example Question #11 : Coordinate Geometry

Example Question #12 : Dsq: Graphing Complex Numbers

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