trigonometry final exam (chapters 7-8)

(a+bi)+(c+di)=

(a+c)+(b+d)i

(a+bi)-(c+di)=

(a-c)+(b-d)i

(a+bi)(c+di)=

(ac-bd)+(ad+bc)i

when are vectors (u and v) orthogonal

when uv=0

how many solutions does a SSA triangle have when the given angle is obtuse

0-1

how many solutions does a SSA triangle have when the given angle is acute

0-2

what type of triangle has a varying number of solutions

SSA

when does vector direction formula change

add pi in Q2/3, add 2pi in Q4

vectors A and B, what is vector AB

c-a,d-b

what law is used to solve an SSS triangle

cosines for largest angle, sines for smaller angle

what law is used to solve an SAS triangle

cosines for remaining side, sines for smaller angle

giving an answer in rectangular form means

evaluating the trig functions

how to divide (a+bi)/(c+di)

multiply the num and denom by the conjugate of the denom

quotient of complex numbers formula (z1/z2)

r1/r2[cos(01-02)+isin(01-02)]

product of complex numbers formula (z1z2)

r1r2[cos(01+02)+isin(01+02)]

powers of complex numbers formula (z^n)

r^n[cos(n0)+isin(n0)]

vector direction formula

tan0=b/a

vector formula

u = a,b

dot product formula (u and v)

u dot v= ac + bd

unit vector formula

u/|u|

angle between two vectors (u and v) formula

uv/|u||v|

(complex numbers) x=

x=rcos0

(complex numbers) y=

y=rsin0

complex number formula in polar form

z=r(cos0+isin0)

complex number formula in rectangular form

z=x+iy

vector magnitude formula

|u|=√a²+b²

imaginary number (i) =

√-1

formula to find a vector, given its magnitude and volume

|u|cos0, |u|sin0