Question

Find the complex number which when multiplied by 2+5i gives 3-7i

Answer 1

see the image for the answer

Answer 2

The required complex number is (-1-i).

Step-by-step explanation:

To find : The complex number which when multiplied by 2+5i gives 3-7i ?

Solution :

Let the required complex number is $a+ib$.

According to question,

$(a+ib)(2+5i)=3-7i$

Solving the equation,

$a+ib=\frac{3-7i}{2+5i}$

Rationalize,

$a+ib=\frac{3-7i}{2+5i}\times \frac{2-5i}{2-5i}$

$a+ib=\frac{6-15i-14i+35i^2}{2^2-(5i)^2}$

$a+ib=\frac{6-29i-35}{4-25i^2}$

$a+ib=\frac{-29-29i}{4+25}$

$a+ib=\frac{-29-29i}{29}$

$a+ib=-1-i$

On comparing,  a=-1 and b=-1

Therefore, the required complex number is (-1-i).

#Learn more

Evaluate: (2√3 + 5i) + (√3 - 7i)

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