hi guys, this is my first post.
wondered is you could help me with these two questions, its the methods i need more than the answers
1) the complex numbers z and w satisfy the simultaneous equations
2z + iw = -1
z - w = 3 + 3i
a) use algebra to find z, giving your answer in the form a+ib, where a and b are real
b) carculate arg z, giving your answer in radians to 2dp.
2) the complex numbers z and w are given by
z = A / (1-i)
w = B / (1-3i)
where A and B are real numbers. given that z + w = i
a) find the value of A and the value of B
b) for these values of A and B, find tan[arg(w-z)]
, so
.
Now equate real and complex coefficients:
and .
From equation 1 we can see .
Substituting into equation 2 gives:
.
And since
.
b)
.
Working out angle in the first quadrant gives:
.
And since will be in the third quadrant, and tangent is positive in the third quadrant, this means
.