Problem IV: Find absolute value(modulus) and phase(argument) of the following complex numbers: I. z=2.
Question 5 [15 marks] The complex numbers z and w are such that w = 1 + a, z =-b-, where a and b are real and positive. Given that wz 3-4, find the exact values of a and b. [7 marks] The complex numbers z and w are such that lz|-2, arg (z)--2T, lwl = 5, arg(w) = 4T. Find the exact values of i. The real part of z and the imaginary part of z ii. The modulus...
(a) Find all numbers z є C such that (z-i)"--64. (b) Find all z E C such that 22 -224i. (c) Find all z E C such that z + z-1-2 . (d) Simplify the expression 1 e i 2 . That is, find the square of the modulus of the complex number 1-e-28 i
Al. Practice with complex numbers: Every complex number z can be written in the form z r + iy where r and y are real; we call r the real part of z, written Re z, and likewise y is the imaginary part of z, y - Im z We further define the compler conjugate of z aszT-iy a) Prove the following relations that hold for any complex numbers z, 21 and 22: 2i Re (2122)(Re z) (Re z2) -...
(2 points) Here are several points on the complex plane: The red point represents the complex number zı = and the blue point represents the complex number Z2 = The "modulus" of a complex number z = x+iy, written [z], is the distance of that number from the origin: z) = x2 + y2. Find the modulus of zi. |zıl = 61^(1/2) We can also write a complex number z in polar coordinates (r, 6). The angle is sometimes called...
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)
Question.4. Find the modulus and argument of sin (θ)-ics() -cos (θ)-i sin (0) COS Given that l-W3 is a root of the equation 2ะ' + az2 +bz + 4-0, find the values of the real numbers, a and b
16. Given complex numbers 21 = 3 – 7i and z2 = -1+9i, find the absolute value of (3z1 + 2z2): | 3z1 + 2z2 = ? (16)
1. Find the magnitude and phase of the following complex numbers: (a) 5+8i 2+31 (b)-5-8i (c) 3+37 (d) 4+2i 4-2i
2 Problem 2: Let z = a + jb be a complex number. (In this course, we use j instead of the more common notation i for the imaginary unit.) Write z as z=rel and determine the magnitude and phase of z in terms of its real and imaginary parts. (10 points)
For the following piecewise-defined function f. find the critical numbers, local extreme values, and absolute extreme values on the closed interval 6, 90 20r109 if 6<214 f(z) 14< <18 8 87 if 18 < z<90 10+237 if Critical number(s) Preview Local minimum value(s) Preview Local maximum value(s) Preview Absolute minimum value: Preview Absolute maximum valug: Preview Points possible: 1 This is attempt 1 of 2. Submit For the following piecewise-defined function f. find the critical numbers, local extreme values, and...