Question

Express 1 by 3 -4i in the form of a + IB​

Answer 1

Answer:

Step-by-step explanation:

1/3-4i

=(3+4i)/(3+4i)*(3-4i)

=3+4i/(3²-16i²)

=(3+4i)/9+16

=(3+4i)/25

Answer 2

The required form is $a+ib=\frac{3}{25}+\frac{-4}{25}i$.

Step-by-step explanation:

Given : Expression $\frac{1}{3+4i}$.

To find : Express expression in the form of a+ib ?

Solution :

Solve the expression by rationalizing,

$a+ib=\frac{1}{3+4i}\times \frac{3-4i}{3-4i}$

$a+ib=\frac{3-4i}{3^2-(4i)^2}$

$a+ib=\frac{3-4i}{9-16i^2}$

$a+ib=\frac{3-4i}{9+16}$

$a+ib=\frac{3-4i}{25}$

$a+ib=\frac{3}{25}-\frac{4i}{25}$

$a+ib=\frac{3}{25}+\frac{-4}{25}i$

On comparing, $a=\frac{3}{25}$ and $b=-\frac{4}{25}$.

Therefore, the required form is $a+ib=\frac{3}{25}+\frac{-4}{25}i$.

#Learn more

Express 5(3+4i)+i(3+4i) in form of a+ib.

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