((1/1-2i) + (3/1+i)) ((3+4i/2-4i)) is equal to :

Question

((1/1-2i) + (3/1+i)) ((3+4i/2-4i)) is equal to : (A) (1/2)+(9/2)i (B) (1/2)-(9/2)i (C) (1/4)-(9/4)i (D) (1/4)+(9/4)i

Tardigrade Admin · Accepted Answer

Let z = ((1/1-2i) + (2/1+i)) ((3+4i/2-4i)) = [(1+i+3-6i/(1-2i)(1+i))] [(3+4i/2-4i)] = [(4-5i/3-i)][(3+4i/2-4i)] = [(32+i/2-14i)] = (32+i/2-14i)×(2+14i/2+14i) = (64+448i+2i-14/4+196) = (50+450i/200) = (1/4) + (9/4)i

Q. $(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$ is equal to :

$\frac{1}{2} + \frac{9}{2} i$

$\frac{1}{2} - \frac{9}{2} i$

$\frac{1}{4} - \frac{9}{4} i$

$\frac{1}{4} + \frac{9}{4} i$

Q. (1−2i1​+1+i3​)(2−4i3+4i​) is equal to :

21​+29​i

21​−29​i

41​−49​i

41​+49​i

Let z=(1−2i1​+1+i2​)(2−4i3+4i​) =[(1−2i)(1+i)1+i+3−6i​][2−4i3+4i​] =[3−i4−5i​][2−4i3+4i​]=[2−14i32+i​] =2−14i32+i​×2+14i2+14i​=4+19664+448i+2i−14​ =20050+450i​=41​+49​i

Q. $(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$ is equal to :

$\frac{1}{2} + \frac{9}{2} i$

$\frac{1}{2} - \frac{9}{2} i$

$\frac{1}{4} - \frac{9}{4} i$

$\frac{1}{4} + \frac{9}{4} i$