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Modulus of a Complex Number

If Rea, Reb...

Question

If $R e (a), R e (b) > 0$ , and $x = | a - b | - | ¯ a + b |$ , then

A

x < 0

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B

x > 0

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C

x \geq 1

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D

0

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Solution

The correct option is A $x < 0$
Lets take $a = a_{1} + i a_{2}, b = b_{1} + i b_{2}$
$x = | (a_{1} + i a_{2}) - (b_{1} + i b_{2}) | + | (a_{1} - i a_{2}) + (b_{1} + i b_{2}) |$
So we can see from above equation
$∣ ∣ ¯ ¯ ¯ a + b ∣ ∣ > | a - b |$
Hence $x < 0$

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