Question

$\huge{\orange{\underline{\pink{\mathscr{Question}}}}}$

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Find the modulus of [(1+i)/(1-i)] – [(1-i)/(1+i)]

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Answer 1

Answer:

Given as

[(1 + i)/(1 – i)] – [(1 – i)/(1 + i)]

Therefore,

Z = [(1 + i)/(1 – i)] – [(1 – i)/(1 + i)]

Now let us simplify, we get

= [(1 + i) (1 + i) – (1 - i) (1 - i)]/(12 – i2)

= [12 + i2 + 2(1)(i) – (12 + i2 – 2(1)(i))]/(1 – (-1)) [Since, i2 = -1]

= 4i/2

= 2i

As we know that for a complex number Z = (a + ib) it’s magnitude is given by |z| = √(a2 + b2)

Therefore,

|Z| = √(02 + 22)

= 2

Thus, the modulus of [(1 + i)/(1 – i)] – [(1 – i)/(1 + i)] is 2.

Hope it's your helpfull

⚡Senior ⚡

Answer 2

Answer:

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