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>
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Explanation:</h2><h2>
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The initial value of this function is the y-intercept. We know that the slope-intercept form of the equation of a line is given by:
Writing our equation in slope intercept form:
So the initial value is:
C
substitute a = - 1 into the expression
- (- 1) - 12(- 1)² = 1 - (12 × 1 ) = 1 - 12 = - 11 → C
7+5(p-p)=7
because 7+5p-5p=7
cross our the 5p because 5p-5p is 0
7=7
~JZ
Hope it helps!
There are 96 possible combinations.
The fundamental counting principle states that the number of total options is given by multiplying the number of possibilities for each option, or
Total choices = choices x choices x ...
4*3*8 = 96
