Express 4-2i1-2i-3-4i2-3i in the form a-b i-a- R- b- R-

4+2i/1 2i+3+4i/2+3i (4+2i)(2+3i)+(3+4i)(1 2i)/(1 2i)(2+3i) 8+4i+6i^2+12i+3 6i+4i 8i^2/2+3i 2i 6i^2 11 2i^2+14i/ 6i^2+i+2 11+2+14i/6+i+2 ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

Express 4+2...

Question

Express $\frac{4 + 2 i}{1 - 2 i} + \frac{3 + 4 i}{2 + 3 i}$ in the form $a + b i, a \in R, b \in R$ .

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Solution

$\frac{4 + 2 i}{1 - 2 i} + \frac{3 + 4 i}{2 + 3 i}$
$\frac{(4 + 2 i) (2 + 3 i) + (3 + 4 i) (1 - 2 i)}{(1 - 2 i) (2 + 3 i)}$
$\frac{8 + 4 i + 6 i^{2} + 12 i + 3 - 6 i + 4 i - 8 i^{2}}{2 + 3 i - 2 i - 6 i^{2}}$
$\frac{11 - 2 i^{2} + 14 i}{- 6 i^{2} + i + 2}$
$\frac{11 + 2 + 14 i}{6 + i + 2}] [∵ i^{2} = - 1]$
$\frac{13 + 14 i}{8 + i}$
multiplying and dividing by 8-i
$\frac{(13 + 14 i) (8 - i)}{(8 + i) (8 - i)}$
$\frac{104 - 13 i - 4 i^{2} + 112 i}{64 - i^{2}}$ [using (a+b)(a-b) = i]
$\frac{104 + 99 i + 14}{64 + 1} = \frac{118 + 99 i}{65}$
$= \frac{118}{65} + \frac{99}{65} i$

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Similar questions

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

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

Q. Represent in a+bi form

\frac{1 + 2 i}{1 - 3 i}

Express the following in standard form: (8 – 4i)-(-2 – 3i)+(-10 + 3i)

Q. Express the following in the form of

a + b i

, where

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. State the value of

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and

b, \frac{3 + 2}{2 - 5 i} + \frac{3 - 2 i}{2 + 5 i}

The conjugate of the complex number $\frac{(2 + 3 i)}{4 i}$ is _____.

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Express 4+2i1−2i+3+4i2+3i in the form a+bi,a∈R,b∈R.

Express $\frac{4 + 2 i}{1 - 2 i} + \frac{3 + 4 i}{2 + 3 i}$ in the form $a + b i, a \in R, b \in R$ .