If z -1-2 i -1-1- i 2- then arg z equalsA- -2B- 0C- -D- none of these

The correct option is B 0 Let z=1+2i/1 (1 i)^2 ⇒ z=1+2i/1 (1+i^2 2i) ⇒ z=1+2i/1 (1 1 2i) ⇒ z=1+2i/1+2i ⇒ z=1 Since point (1, 0) lies on the positive directi ...

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Byju's Answer

Standard XII

Mathematics

Argument of a Complex Number

If z =1+2 i /...

Question

If $z = \frac{1 + 2 i}{1 - (1 - i)^{2}}$ , then arg (z) equals

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$\frac{π}{2}$

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$π$

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none of these

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Solution

The correct option is A
0

$Let z = \frac{1 + 2 i}{1 - (1 - i)^{2}} \Rightarrow z = \frac{1 + 2 i}{1 - (1 + i^{2} - 2 i)} \Rightarrow z = \frac{1 + 2 i}{1 - (1 - 1 - 2 i)} \Rightarrow z = \frac{1 + 2 i}{1 + 2 i} \Rightarrow z = 1$

Since point (1, 0) lies on the positive direction of real axis, we have :

arg (z) = 0

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If z=1+2i1−(1−i)2, then arg (z) equals

The correct option is A 0 Let z=1+2i1−(1−i)2⇒ z=1+2i1−(1+i2−2i)⇒ z=1+2i1−(1−1−2i)⇒ z=1+2i1+2i ⇒ z=1 Since point (1, 0) lies on the positive direction of real axis, we have : arg (z) = 0

If $z = \frac{1 + 2 i}{1 - (1 - i)^{2}}$ , then arg (z) equals