All categories

3 years ago

What is the product of 5−2i and 3−4i? Enter your answer, in standard form, in the box

Mathematics

1 answer:

Lelechka [254]3 years ago

7 0

Answer:

$\boxed{7-26i}$

Step-by-step explanation:

The binomials are multiplied in the usual way, using FOIL or the distributive property:

(5 -2i)(3 -4i) = 15 -20i -6i +8i²

Since i² = -1, this becomes ...

= 15 -20i -6i -8 = 7 -26i

You might be interested in

Given points A (-3,-4) and B (2,0), points P (-1,-12/5) partitions line AB in the ratio

kvv77 [185]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&A&(~ -3 &,& -4~) 
&P&(~ -1 &,& -\frac{12}{5}~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AP=\sqrt{[-1-(-3)]^2+[-\frac{12}{5}-(-4)]^2}
\\\\\\
AP=\sqrt{(-1+3)^2+(-\frac{12}{5}+4)^2}\implies AP=\sqrt{2^2+\left( \frac{8}{5} \right)^2}
\\\\\\
AP=\sqrt{4+\frac{64}{25}}\implies AP=\sqrt{\cfrac{164}{25}}\implies AP=\cfrac{\sqrt{164}}{\sqrt{25}}
\\\\\\
\boxed{AP=\cfrac{2\sqrt{41}}{5}}$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&P&(~ -1 &,& -\frac{12}{5}~) 
&B&(~ 2 &,& 0~)
\end{array}
\\\\\\
PB=\sqrt{[2-(-1)]^2+[0-\left(-\frac{12}{5} \right)]^2}
\\\\\\
PB=\sqrt{(2+1)^2+\left( \frac{12}{5} \right)^2}\implies PB=\sqrt{9+\frac{144}{25}}\implies PB=\sqrt{\cfrac{369}{25}}
\\\\\\
PB=\cfrac{\sqrt{369}}{\sqrt{25}}\implies \boxed{PB=\cfrac{3\sqrt{41}}{5}}$

so, let's check the ratio of AP:PB

$\bf AP:PB\implies \cfrac{AP}{PB}\implies \cfrac{\frac{2\sqrt{41}}{5}}{\frac{3\sqrt{41}}{5}}\implies \cfrac{2\underline{\sqrt{41}}}{\underline{5}}\cdot \cfrac{\underline{5}}{3\underline{\sqrt{41}}}\implies \cfrac{2}{3}$

7 0

3 years ago

A sprinter travels a distance of 100 m in a time of 11.21 seconds.

sergiy2304 [10]

Answer:

distance travelled by sprinter = 100 m

Time taken = 11.21sec

∵speed = distance/time taken

= 100/9.83

= 10.17 m/s

Now we know, 1 km/h = 1000/3600 m/s

so, 1 m/s = 3600/1000 km/h = 18/5 km/h

∴ 10.17 m/s = 10.17 × 18/5 = 10.17 × 18/5 = 36.612 km/h

Hence, average speed = 36.612 km/h

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Write the equation for the inverse function of y=0.4x-1.2

loris [4]

I think it is 0.4/0.4 but I'm not sure

7 0

2 years ago

Can someone ONE person tutor me in math?plsss

Rina8888 [55]

Answer:

I can

Step-by-step explanation:

I'm taking precalculus currently

5 0

2 years ago

Read 2 more answers

Write an expression to represent: the product of 5 and a number decreased by 3.

Maru [420]

Answer:

(n) (5) - 3

5n - 3

7 0

3 years ago