Simplify 1-1-2i-3-1-i 3-4i-2-4i

The correct option is C 1/4+9/4i. Simplifying, we get nbsp; 1+i+3 6i1+i 2i+2 4 5i3 i ...(i)Hence 4 5i3 i.3+4i2 4i =12+16i 15i+206 12i ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

Simplify 1/...

Question

Simplify $(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$

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

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

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

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- \frac{1}{4} + \frac{9}{4} i .

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Solution

The correct option is C $\frac{1}{4} + \frac{9}{4} i .$
Simplifying, we get
$\frac{1 + i + 3 - 6 i}{1 + i - 2 i + 2}$
$\frac{4 - 5 i}{3 - i}$ ...(i)
Hence
$\frac{4 - 5 i}{3 - i} . \frac{3 + 4 i}{2 - 4 i}$
$= \frac{12 + 16 i - 15 i + 20}{6 - 12 i - 2 i - 4}$
$= \frac{32 + i}{2 - 14 i}$
$= \frac{(32 + i) (2 + 14 i)}{200}$
$= \frac{64 + 448 i + 2 i - 14}{200}$
$= \frac{50 + 450 i}{200}$
$= \frac{1 + 9 i}{4}$ .

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Similar questions

(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i}) =

Q. Solve:

(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})

Q. Rationalise and simplify

\frac{\sqrt{1 + 4 i} + \sqrt{1 - 4 i}}{\sqrt{1 + 4 i} - \sqrt{1 - 4 i}}

Q. Simplify

(2 + 8 i) (1 - 4 i) - (3 - 2 i) (6 + 4 i)

(Note

: i = \sqrt{- 1}

)

Express the following complex numbers in the standard form a + i b :

$(i) (1 + i) (1 + 2 i) (i i) \frac{3 + 2 i}{- 2 + i} (i i i) \frac{1}{(2 + i)^{2}} (i v) \frac{1 - i}{1 + i} (v) \frac{(2 + i)^{3}}{2 + 3 i} (v i) \frac{(1 + i) (1 + \sqrt{3 i})}{1 - i} (v i i) \frac{2 + 3 i}{4 + 5 i} (v i i i) \frac{(1 - i)^{3}}{1 - i^{3}} (i x) (1 + 2 i)^{- 3} (x) \frac{3 - 4 i}{(4 - 2 i) (1 + i)} (x i) (\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{3 - 4 i}{5 + i}) (x i i) \frac{5 + \sqrt{2 i}}{1 - \sqrt{2 i}}$

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Simplify (11−2i+31+i)(3+4i2−4i)

The correct option is C 14+94i.Simplifying, we get 1+i+3−6i1+i−2i+24−5i3−i ...(i)Hence4−5i3−i.3+4i2−4i=12+16i−15i+206−12i−2i−4=32+i2−14i=(32+i)(2+14i)200=64+448i+2i−14200=50+450i200=1+9i4.

Simplify $(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$