Write the cojugate of 2- i -1-2 i 2-

Given that, z=2 i/(1 2i)^2=2 i/1+4i^2 4i =2 i/1 4 4i=2 i/ 3 4i =(2 i)/ (3+4i)= [(2 i)(3 4i)/(3+4i)(3 4i) ] =(6 8i 3i+4i^2/9+16 )= 11i+2/25 = 1/25(2 11i)⇒ z= ...

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Byju's Answer

Standard XII

Mathematics

Conjugate of a Complex Number

Write the coj...

Question

$Write the cojugate of \frac{2 - i}{(1 - 2 i)^{2}} .$

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Solution

Given that, $z = \frac{2 - i}{(1 - 2 i)^{2}} = \frac{2 - i}{1 + 4 i^{2} - 4 i}$

$= \frac{2 - i}{1 - 4 - 4 i} = \frac{2 - i}{- 3 - 4 i} = \frac{(2 - i)}{- (3 + 4 i)} = - [\frac{(2 - i) (3 - 4 i)}{(3 + 4 i) (3 - 4 i)}] = (\frac{6 - 8 i - 3 i + 4 i^{2}}{9 + 16}) = - \frac{- 11 i + 2}{25} = \frac{- 1}{25} (2 - 11 i) \Rightarrow z = \frac{1}{25} (- 2 + 11 i) ∴ ¯ z = \frac{1}{25} (- 2 + 11 i) = \frac{- 2}{25} - \frac{11}{25} i$

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Similar questions

Q. Evaluate and write in standard form:

{(- 3 + 2 i)}^{2} - 3 (3 - i) (- 2 + 2 i)

, where

i^{2} = - 1

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

Q. The conjugate complex number of

\frac{2 - i}{(1 - 2 i)^{2}}

Q. Find the conjugate of

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

Q. Put the following in the form of A + iB :

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

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Write the cojugate of 2−i(1−2i)2.

Given that, z=2−i(1−2i)2=2−i1+4i2−4i =2−i1−4−4i=2−i−3−4i=(2−i)−(3+4i)=−[(2−i)(3−4i)(3+4i)(3−4i)]=(6−8i−3i+4i29+16)=−−11i+225=−125(2−11i)⇒ z=125(−2+11i)∴ ¯z=125(−2+11i)=−225−1125i

$Write the cojugate of \frac{2 - i}{(1 - 2 i)^{2}} .$