Assertion A- The principal amplitude of complex number x - ix is -4-Reason R- The principal amplitude of a complex number x - iy is -4 if y - x-

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Standard X

Mathematics

Formula for Sum of n Terms of an AP

Assertion A: ...

Question

Assertion (A): The principal amplitude of complex number $x + i x$ is $\frac{π}{4}$ .
Reason (R): The principal amplitude of a complex number $x + i y$ is $\frac{π}{4}$ if $y = x$ .

Both A and R are true and R is the correct explanation of A

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A is true R is false

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A is false, R is true

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Both A and R are false

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Solution

The correct option is B Both A and R are true and R is the correct explanation of A
Assertion : $a r g (x + i x) = a r g \frac{x}{x}$ $= \frac{π}{4}$

Reason : if $y = x$ then $a r g (x + i y) = \frac{π}{4}$

$∴$ Both Assertion and reason are true and Reason is the correct explanation of Assertion.
Hence, option A is correct.

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Assertion (A): The principal amplitude of complex number x+ix is π4.Reason (R): The principal amplitude of a complex number x+iy is π4 if y=x.

The correct option is B Both A and R are true and R is the correct explanation of AAssertion : arg(x+ix)=argxx =π4Reason : if y=x then arg(x+iy)=π4∴ Both Assertion and reason are true and Reason is the correct explanation of Assertion.Hence, option A is correct.

Assertion (A): The principal amplitude of complex number $x + i x$ is $\frac{π}{4}$ .
Reason (R): The principal amplitude of a complex number $x + i y$ is $\frac{π}{4}$ if $y = x$ .