trig
posted by BreAnne .
6. Compute the modulus and argument of each complex number. I did ac and f.
D. 5
E. 5+5i
G. 34i
7. Let z= 5sqrt3/2+5/2i and w= 1+sqrt3i
a. convert z and w to polar form
b. calculate zw using De Moivres Theorem
c. calculate (z/w) using De M's theorem
Please help with these two problems? I did 16 and 910 already.

6. I will do E, you try the others the same way
let z = 5 + 5i
modulus z = z = √((5)^2 + 5^2) = √50 = 5√2
argument:
tanØ = 5/5 = 1, where Ø is in quad II
Ø = 135°
G. is done the same way
for D, think of it as 5 + 0i 
7.
z = 5√3/2 + 5/2i
= 5(√3/2 + (1/2)i )
argument :
tan Ø = (1/2) / (√3/2), where Ø is in II
tan Ø = 1/√3
Ø = 150° or 5π/6 radians
z = 5(cos 150° + isin 150°) or 5(cos 5π/6 + isin 5π/6)
in the same way:
w = √10(cos 60°+ isin 60°) or √10(cos π/3 + isin π/3) 
b) to multiply two complex numbers in complex form
if u = r1(cos Ø1 + isinØ1) and v = r2(cosØ2 + isinØ2)
then uv = r1r2(cos(Ø1+Ø2) + isin(Ø1+Ø2)
and u/v = r1/r2 (cos(Ø1Ø2) + isin(Ø1Ø2)
so
(z)(w) = 5√10(cos (150+60) + isin(150+60)
= 5√10(cos 210° + isin 210°)
do z/w using the above definition.
Respond to this Question
Similar Questions

maths
How do you convert degrees to radians? what's the modulus and the principle argument (complex n°) 
complex numbers
how do you work out the the form a+ib when you are given the modulus and argument i.e. modulus=5,argument=pi/2 
precalculus
convert the equation y^2 = 2x x^2 into polar form. convert the equation r = 2tan(theta) into rectangular form. I'm not really sure what either of these mean. I vaguely understand polar coordinates, but I'm not sure how to convert … 
precalc
Suppose that z1=68i. Find: A. The Trig Form of the complex number z1, where your theta is in degrees. B. The Trig form of z1*z2, where z2=5[cos(60degrees)+isin(60degrees)] C. The Trig Form of (z1)^4 
Trig
Convert 2xy = 1 to polar form. 
TRIGONOMETRY
Can someone please show me step by step how to calculate the modulus and the argument for these complex numbers? 
trig
Write the complex number in trigonometric form, using degree measure for the argument. 12  16i 
Mathematics
Express the Complex Number 1i in polar form. how is complex no expressed in polar form? 
Trig (math)
1.) Find all solutions of the equation. Leave answers in trigonometric form. x^2 + 1  sqrt3i = 0 2.) Give the rectangular coordinates for the point. (9, 2pi/3) 3.) The rectangular coordinates of a point are given. Express the point … 
Maths
Convert the complex no. In polar form : 1i rcosΘ =1 rsinΘ=1 r=√a2+b2 r=√(1)2+(1)2 r=√2 TanΘ=b/a =1/1 =1 After all this what i have to do to find out value of Θ?