Write the following complex numbers in polar form, as ??^??.
1/3+4i
Write the following complex numbers in polar form, as ??^??.
1/3+4i
Solutions
Expert Solution
We here asked to find the modulus amplitude form or we can say
the polar form of tge given complex number. So we simply find the
modulus and the amplitude to find the required form. The detailed
method is given below:
Solve the following equations in complex numbers and write your
answer in polar and rectangular form.
(a) z2 − i = 0 in C
(b) z7 + z6 + z5 +
z4 + z3 + z2 + z = 0
(c) e2z + 2ez = −2
(d) z + 1 / z−1 = eiπ/3
1. Express the following complex numbers in cartesian form x +
jy: 1/2 e jπ , 1/2 e −jπ , √ 2e j9π/4 , √ 2e −j9π/4
2. Express the following complex numbers in polar form rejθ with
−π < θ ≤ π: 5, −2, 1/2 − j √ 3/2, (1 + j)/(1 − j).
PLEASE ANSWER WITH FULL STEPS AND CORRECT.
Convert the complex number to polar form rcisθ.
(a) For z=−1+i
the modulus of zis r=, and the principal argument is θ =.
(b) For z=−33‾√−3i
the modulus of zis r=, and the principal argument is θ =.
(c) For z=−2
the modulus of zis r=, and the principal argument is θ =.
(d) For z=−3i
the modulus of zis r=, and the principal argument is θ= .
(a) look at these the complex numbers z1 = − √ 3 + i and z2 =
3cis(π/4). write the following complex numbers in polar form,
writing your answers in principal argument:
i. z1
ii. z1/|z1|. Additionally, convert only this answer into
Cartesian form.
iii. z1z2
iv. z2/z1
v. (z1) -3
vi. All complex numbers w that satisfy w 3 = z1.
(b) On an Argand diagram, sketch the subset S of the complex
plane defined by S = {z...
Due October 25. Let R denote the set of complex numbers of the
form a + b √ 3i, with a, b ∈ Z. Define N : R → Z≥0, by N(a + b √
3i) = a 2 + 3b 2 . Prove: (i) R is closed under addition and
multiplication. Conclude R is a ring and also an integral domain.
(ii) Prove N(xy) = N(x)N(y), for all x, y ∈ R. (ii) Prove that 1,
−1 are the...