Question

what is the value of imaginary part in 1/(5 + 6i) ?
a)6 b) 5/61 c) -6/61 d)5​

Answer 1

Answer:

I think option a 6 is correct answer

Answer 2

Answer:

The correct option for the imaginary part of the given complex number is option (c): $-\frac{6}{61}$.

Step-by-step explanation:

The complex number given to us is:

$Z=\frac{1}{5+6i}$

Now, we know that for any complex number, we need to make the denominator a real number and move the complex part to the numerator to know the real and imaginary part.

So, multiplying and dividing the given complex number by the conjugate of $5+6i$, i.e., $5-6i$, we get:

$Z=\frac{1}{5+6i}\times \frac{5-6i}{5-6i}$

$Z=\frac{5-6i}{(5+6i)(5-6i)}$

Now, using the identity: $(a-b)(a+b)=a^2-b^2$ and also, the identity: $i^2=-1$, we get:

$Z=\frac{5-6i}{(5)^2-(6i)^2}$

$Z=\frac{5-6i}{25+36}$

or we can say:

$Z=\frac{5-6i}{61}$

Representing this in the general form of $Z=a+ib$ with the imaginary part being 'b', we get:

$Z=\frac{5}{61}-\frac{6}{61}i$

Now, by comparison, we get:

$b=-\frac{6}{61}$

So, option (c) is the correct answer.