The argument of complex number Z -3- i -2 i -1- i 2A- -tan -1 3B- - - 4C- -tan -1 5D- tan -1 5

(1+i)^2 = 1 + i^2 + 2i = 2i Z = 3+i/2i + 2i = 3+i/4i * i/i = 1+3i/ 4 = 1 3i/4 if x +iy = 1 3i/4 ⇒ (x,y) = (1/4 , 3/4) is in 4^th quadrant So, θ = [tan ...

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Standard XII

Mathematics

Algebra of Complex Numbers

The argument ...

Question

The argument of complex number Z = $\frac{3 + i}{2 i + (1 + i)^{2}}$

π/4

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-tan^-15

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tan^-15

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-tan^-13

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Solution

The correct option is D
-tan^-13

$(1 + i)^{2}$ = 1 + $i^{2}$ + 2i = 2i

Z = $\frac{3 + i}{2 i + 2 i}$ = $\frac{3 + i}{4 i}$ * $\frac{i}{i}$ = $\frac{- 1 + 3 i}{- 4}$ = $\frac{1 - 3 i}{4}$

if x +iy = $\frac{1 - 3 i}{4}$ $\Rightarrow$ (x,y) = $(\frac{1}{4}, \frac{- 3}{4})$ is in $4^{t h}$ quadrant

So, $θ = [{tan}^{- 1} | \frac{y}{x} |]$

= - ${tan}^{- 1}$ 3

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The argument of complex number Z = 3+i2i+(1+i)2

The correct option is D -tan-1 3 (1+i)2 = 1 + i2 + 2i = 2i Z = 3+i2i+2i = 3+i4i * ii = −1+3i−4 = 1−3i4 if x +iy = 1−3i4 ⇒ (x,y) = (14,−34) is in 4th quadrant So, θ=[tan−1|yx|] = -tan−13

The argument of complex number Z = $\frac{3 + i}{2 i + (1 + i)^{2}}$