When you multiply two complex numbers given in polar form, the argument of the product is the sum of the arguments of the factors. Meanwhile, the modulus of the product is the product of the moduli of the factors.
In this case, you'd have

and the modulus would simply be

. Since

we would expect the final product to fall in the first quadrant.
Answer:
(a <em><u>s</u></em><em><u>q</u></em><em><u>u</u></em><em><u>a</u></em><em><u>r</u></em><em><u>e</u></em><em><u> </u></em><em><u>+</u></em><em><u>7</u></em><em><u>a</u></em><em><u>+</u></em><em><u>1</u></em><em><u>2</u></em><em><u>)</u></em><em><u> </u></em><em><u>÷</u></em><em><u>(</u></em><em><u>a</u></em><em><u>+</u></em><em><u>3</u></em><em><u>)</u></em>
Answer:
(A)6 kilometers
Step-by-step explanation:
First, we determine the value of a using Pythagoras Theorem.

Therefore:
Distance along the long route = 8 + 15 =23 km
Distance along the shortcut =17 km
Difference =23-17 =6km
Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.
Answer:
The family will pay 34722 cents more if they take the van
Step-by-step explanation:
Given
Van = 12 miles per gallon
Sedan = 36 miles per gallon
Distance = 2500 miles
Gas = $2.50 per gallon
First, we need to determine the number of gallons that'll be used by both vehicles
This is done by dividing total distance by number of miles per gallon


Next, is to multiply this by the cost of gas per gallon;
This gives the total spendable amount on both vehicles






Next is to get the difference between these amounts


Multiply by 100 to convert to cents


(Approximated)
Hence;
<em>The family will pay 34722 cents more if they take the van</em>