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
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
z = -5√3/2 + 5/2i
= 5(-√3/2 + (1/2)i )
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(Ø1-Ø2) + isin(Ø1-Ø2)
(z)(w) = 5√10(cos (150+60) + isin(150+60)
= 5√10(cos 210° + isin 210°)
do z/w using the above definition.
maths - How do you convert degrees to radians? what's the modulus and the ...
complex numbers - how do you work out the the form a+ib when you are given the ...
calculus - find the modulus and the argument of the following complex numbers: ...
trig - Write the complex number in trigonometric form, using degree measure for ...
TRIGONOMETRY - Can someone please show me step by step how to calculate the ...
Pure Mathematics - Find the modulus and principal argument of the complex ...
trig - What is the trigonometric notation for 3-3(sqrt3i)?
chemistry - DrBob222 - For this question can u please explain steps 3 and 4 4.0 ...
precalc - Suppose that z1=6-8i. Find: A. The Trig Form of the complex number z1...
Trig/Precalc - The system of equations: |z-2-2i|=sqrt(23), |z-8-5i|=sqrt(38) has...