Which fraction do you multiply by to simplify 5/ 4 - 3i ?

1 answer:

3 0

So I assume
$\frac{5}{4-3i}$

If so. Let us begin.

$\mathrm{Multiply\:by\:the\:conjugate}\:\frac{4+3i}{4+3i} \ \textgreater \ \frac{5\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)} \ \textgreater \ \left(4-3i\right)\left(4+3i\right)$

$\mathrm{Apply\:complex\:arithmetic\:rule}:\ \left(a+bi\right)\left(a-bi\right)=a^2+b^2$
$Where\;a=4,\:b=-3 \ \textgreater \ 4^2+\left(-3\right)^2 \ \textgreater \ Refine \ \textgreater \ 25$

$\frac{5\left(4+3i\right)}{25} \ \textgreater \ \mathrm{Cancel\:the\:common\:factor:}\:5 \ \textgreater \ \frac{4+3i}{5}$

$Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number$
$\frac{4}{5}+\frac{3}{5}i\;is\;our\;answer!$

Hope this helps!

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What is the point of intercection of lines y=x and y=2x+1

12345 [234]

Answer:

(-1, -1)

Step-by-step explanation:

Let's set these two equations equal to each other to solve the system:

x = 2x + 1

Solving for x, we get x = -1

Plug this value of x back into any of the two equations to get y: y = 2 * (-1) + 1 = -1.

Thus, the point of intersection is (-1, -1).

Hope this helps!