For polar form you need to find the modulus (length of the vector) and the argument (angle of the vector) and present in form rcis(Arg) or re^Argi
start with the modulus r=sqrt(a^2 +b^2)
=sqrt(-2^2 +2^2)
= sqrt(4+4)
=sqrt(8)
=2sqrt(2)
next the argument, firstly arg=tan(b/a)
= tan(2/2)
=tan(1)
=pi/4 . (exact values table)
Now consider the quadrant the complex number is in, as it is (-2,2) it is in the second quadrant and as such your Arg value is:
Arg=pi-arg
= pi-pi/4
= 3pi/4
add it all together and your complex number in polar form is:
2sqrt2cis(3pi/4)
note: cis is short hand for cos(x)+isin(x), it is possible your tutor would rather you use the complex exponential form which is simply re^Argi and your answer would look like:
2sqrt2e^(3pi/4)i
Also notice the difference between arg and Arg as this often slips students up and always present Arg in prinicple argument form ie -pi<Arg<pi
Hopefully this has been clear enough and good luck
Answer:
AE = 70
Step-by-step explanation:
Given that ACE is a triangle and B , D , F are mid-points of AC, CE, AE respectively.
⇒ BF, FD, BD are mid-segments.
Mid-segment is a line segment joining mid points of two sides of a triangle,
And it as two properties :
1) mid-segment is always parallel to the third side
2) mid-segment is half in length of the third side
⇒ Here, BD is the mid-segment and is parallel to third side AE
And also BD is half of AE
⇒ AE = 2×BD = 2×35
⇒ AE = 70.
You gotta increase the points that’s a big question for 5 points
(12 gallons)/(5 minutes<span>) = (2.4 </span>gallons<span>)/(1 minute)
So it'd be 2.4 gallons a minute.
Have a nice day! :D</span>
Answer:
You did it correctly that's the right answer
Great Job!