Solve the following system of equations for z1 and z2 (-5 + 3i)21 + 4iz2 =...
please use complex conjugate to find 21 = 2 + 3i, z2 = 5 – 4i, please use complex conjugate to find 2 = ? 21 = -4+ 21, z2 = 5 – 3i, 72 = ? 21 = –4 + 2i, z2 = 5 – 3i, 21 – 21 = ? + 21 = -4 + 2i, z2 = 5 – 3i, 2171 = ?
Write 21 and 22 in polar form. 21 = 5 + 5i, z2 = 16 Z1 = x 22 = x Find the product 2122 and the quotients 1 and 1 (Express your answers in polar form.) Z2 2122 x 21 22 1 21 = X
Find R and angle. Z1 =8+3i, Z2 =2+3i, Z3 =9-((2)^1/2 )i. (vi) z = TEM (vii) 2 = 22 + 231
Given that z1 = 6−3 i and z2 = 3−11 i, find the following in the form x + y i _ Z1 = _ Z1 Z2 = Z1/Z2=
Problem 1: Consider the following complex numbers: Z1 = 2 + j4 Z2 = 5e3 a) Write zi in polar form b) Write ze in rectangular form c) Plot the product of zı & z2 in the complex plane with x(0) = 0.3 Problem 2: Consider the system: dx/dt = -3x a) Solve the initial value problem b) Plot the resulting function
Find the complex numbers w and z which solve the system of equations (-1+i)w + (-2-3i)z = -12 - 3i (-2+3i)w +(-1+i)z = 0 +10i (Hint: Check your solution by substituting back in)
Describe by words and/or pictures, z, z1, z2, such that: 1) |z+5| = 3 2) -3 < Re(z) < 5 3) Arg(z1) = Arg(z2) 4) |z1| = |z2| 5) Im(z1 z*2) = 0 6) |z| = |z*| ** z* = "complex conjugate of z"
3. (a) Let z1,z2, z3 € C, prove the following identity: (21 - 22)(22 – 23)(23 – £1) = (22 - 23)+23(23 – £1)+23(21 - 22). (b) In AABC, P is a point on the plane II containing A, B and C. Prove that aPA +bPB2 +cPC2 > abc.
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
Please read the question thoroughly and show all your work, please. 2. Let z1=4+4i, z2=-5-5i. Find the trig form of z1 and 22. Then, find 21/22 and 2122