Question

Express the complex number 1+yi in the form x+yi where X and Y are real numbers.​

Answer 1

Answer:

Correct option is

D

π−2

z=x+iy

A={z:∣z∣≤2}

⟹

x

2

+y

2

≤2

or x

2

+y

2

≤4

⟹z lies on or inside the circle x

2

+y

2

=4

B={z:(1−i)z+(1+i)

z

≥4}

⟹(1−i)(x+iy)+(1+i)(x−iy)≥4

⟹x+iy−ix+y+x−iy+ix+y≥4

⟹x+y≥2

Area of region A∩B is the shaded region shown in Fig. 3.19

Area =

4

π(2)

2

−

2

1

×2×2=π−2

Ans: D

solution

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