1. The answer is C. cos180=-1, sin180=0. 2*(cos180+i*sin180)=2*(-1+0)=-2. Check every other answer, none of which gets -2.
2. The answer is C. cos270=0, sin270=-1. (You can draw out these angles to see). 2*(cos270+i*sin270)=2*(0-i)=-2i, as desired. Other choices don't work.
3. Answer A. Modulus of z is \sqrt(6^2+(-6)^2)=6*\sqrt(2). <span>The </span>angle<span> of the </span>point<span> on the complex </span>plane<span> is the </span>inverse tangent<span> of the complex portion over the real portion. Theta=arctan(-6/6), and arctan(-1)=-pi/4, so theta=-pi/4=-pi/4+2pi=7pi/4. So A is the correct answer.
4. The answer is A. As above, cos270=0, sin270=-1. 3(cos270+sin270*i)=3*(0-i)=-3i. This problem is similar to question 2.
5. </span>z1 = 7(cos 40° + i sin 40°), and z2 = 6(cos 145° + i sin 145°). z1*z2=7*6*(cos 40° + i sin 40°)*(cos 145° + i sin 145°)=42*(cos40*cos145-sin40*sin145+i*sin40*cos145+i*sin145*cos40). Use formula for sum/difference formula of cosines, cos40*cos145-sin40*sin145=cos(40+145)=cos185. Again, sin40*cos145+sin145*cos40=sin(40+145)=sin185. The answer is <span>42(cos 185° + i sin 185°).</span>
Answer:
c
Step-by-step explanation:
- right because it has a 90-degree-angle
- and isosceles because it has two equal sides (the two marked ones - congruent sides)
Let's see here. Sarah is one person. Her three friends are three more. That means 4 people are decorating picture frames. However, we only have 3 rolls of ribbon! We can give an entire roll to each person, but one person would have no roll to decorate with! What do we do? We have to divide this. By definition, divide means to separate something(in this case, ribbon rolls) into (equal) parts. So, we must divide them so everyone gets an EQUAL ribbon roll length.
Answer:
f(x)=-4x+/4
let y=f(x)
y=-4x+4
interchange the role of x & y
x=-4y+4
x-4=-4y
(x-4)/-4=y
y=-(x-4)/4
f-¹(x)=-(x-4)/4
yeah you are right
Answer:
28 is 11/60
29 is 7/30
Step-by-step explanation:
