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write the multiplicative inverse of {{ 3 }}{2} - {1}{2}i

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write the multiplicative inverse of $\frac{3}{2} - \frac{1}{2} i$

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write the multiplicative inverse of

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

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Text solutionVerified

Given imaginary number is

a = \frac{3}{2} - \frac{1}{2} i

multiplicative inverse(b) of a number(a) is defined by

a \times b = 1

or

b = \frac{1}{a}

hence,

b = \frac{1}{\frac{3}{2} - \frac{1}{2} i}

or

b = \frac{2}{3 - i}

multiply and divide above equation by

(3 + i)

we get

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

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

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

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

b = \frac{3 + i}{2}

(multiplicative inverse of given number a)

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Question Text	write the multiplicative inverse of $\frac{3}{2} - \frac{1}{2} i$
Answer Type	Text solution:1
Upvotes	150