Which of the following are correct? I. Modulus of $\frac{1+{i}}{1-{i}}$ is 1. II. Argument of $\frac{1+i}{1-i}$ is $\frac{\pi}{2}$. III. Modulus of $\frac{1}{1+{i}}$ is $\sqrt{2}$. IV. Argument of $\frac{1}{1+{i}}$ is $\frac{\pi}{4}$.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Medium

1 of 1

Application +4 | -1

Which of the following are correct?

I. Modulus of

\frac{1+{i}}{1-{i}}

is 1.

II. Argument of

\frac{1+i}{1-i}

\frac{\pi}{2}

.

III. Modulus of

\frac{1}{1+{i}}

\sqrt{2}

.

IV. Argument of

\frac{1}{1+{i}}

\frac{\pi}{4}

View answer and explanation

Correct option: A

I and II are correct

Option A (I and II are correct) is correct because the modulus of (1+i)/(1-i) is 1 and its argument is π/2, while statements III and IV are incorrect.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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