The conjugate of the complex number 2-3 i-4 i iA- 3-2 i - 4B- 3-2 i - 4C- 2 i -3 - 4D- 2 i -3 - 2

The correct option is A (3 + 2i)/4 Let z = 2 + 3i/4i × 4i/4i = 8i 12/ 16 = 1/4(2i 3) = 1/4(3 2i) Conjugate z = 1/4(3 + 2i) ...

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Byju's Answer

Standard XI

Mathematics

Conjugate of a Complex Number

The conjugate...

Question

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

(3 + 2i)/4

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(3 - 2i)/4

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(2i - 3)/4

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(2i - 3)/2

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Solution

The correct option is A
(3 + 2i)/4

Let z = $\frac{2 + 3 i}{4 i}$ $\times$ $\frac{4 i}{4 i}$

= $\frac{8 i - 12}{- 16}$ = $\frac{- 1}{4}$ (2i - 3)

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

Conjugate $¯ ¯ ¯ z$ = $\frac{1}{4}$ (3 + 2i)

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Similar questions

Q. Find the conjugate of

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

Q. 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

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. Show that

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

is real.

Q. The modulus of the complex number

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

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The conjugate of the complex number (2+3i)4i is _____.

The correct option is A (3 + 2i)/4 Let z = 2+3i4i × 4i4i = 8i−12−16 = −14(2i - 3) = 14(3 - 2i) Conjugate ¯¯¯z = 14(3 + 2i)

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

The correct option is A
(3 + 2i)/4

Let z = $\frac{2 + 3 i}{4 i}$ $\times$ $\frac{4 i}{4 i}$

= $\frac{8 i - 12}{- 16}$ = $\frac{- 1}{4}$ (2i - 3)

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

Conjugate $¯ ¯ ¯ z$ = $\frac{1}{4}$ (3 + 2i)