Put the following in the form of A - iB - 11 - 2i - 31 - i3 - 4i2 - 4i

( 11 2i +31+i ) ( 3+4i2 4i ) ( (1+i)+3(1 2i)(1 2i)(1+i) ) ( 3+4i2 4i ) ( 4 5i3 i ) ( 3+4i2 4i ) 32+i2 14i 32+i2 14i×2+14i2+14i 14+ ...

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Byju's Answer

Standard XII

Mathematics

Purely Imaginary

Put the follo...

Question

Put the following in the form of A + iB :
$(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$

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Solution

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

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

$(\frac{4 - 5 i}{3 - i}) (\frac{3 + 4 i}{2 - 4 i})$

$\frac{32 + i}{2 - 14 i}$

$\frac{32 + i}{2 - 14 i} \times \frac{2 + 14 i}{2 + 14 i}$

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

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Similar questions

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

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

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

Q. Simplify

(\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. If

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

, then

a^{2} + b^{2} =

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Put the following in the form of A + iB :(11−2i+31+i)(3+4i2−4i)

(11−2i+31+i)(3+4i2−4i)((1+i)+3(1−2i)(1−2i)(1+i))(3+4i2−4i)(4−5i3−i)(3+4i2−4i)32+i2−14i32+i2−14i×2+14i2+14i14+9i4

Put the following in the form of A + iB :
$(\frac{1}{1 - 2 i} + \frac{3}{1 + i}) (\frac{3 + 4 i}{2 - 4 i})$