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4-3i 11. (8 pts) Forz 4-3i much as possible, writin work. i and w 7- i,...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
2iz-1 If f(2) = 27251 2-3i a) Find and simplify f'(z) b) Find f'(1 + i) and write the answer in cartesian form (a + bi).
(1 point) Suppose pP(z) 5x2+ z+3 (a) Simplify as much as possible: p(-1)=7 help (numbers) (b) Simplify as much as possible: -p(1)= | help (numbers) (c) Are p(-1) and p(1) equal? No (1 point) Suppose pP(z) 5x2+ z+3 (a) Simplify as much as possible: p(-1)=7 help (numbers) (b) Simplify as much as possible: -p(1)= | help (numbers) (c) Are p(-1) and p(1) equal? No
Find w=a +bi = VE , where a and b are real numbers. 7601 - 11 Answer: w= w=
Perform the indicated operation and write the answer in the form a +bi, where a and b are real numbers. 28) (6-5i)(7 +3i) A) -15;2 - 171 +42 B) 57 - 171 C) 27 - 531 D) 57 +171 Write the quotient in the form a +bi. 9 +41 29) 2-4i B) -1.4, C) -1 5 Use De Moivre's theorem to simplify the expression. Write the answer in a +bi form. 30) (3 (cos 120° + i sin 120°))4 A)...
Please solve #3 and #4. Show work if possible thanks! 2. Assume variables represent positive real li a. Simplify, leaving in radical form. 너2 2 7 b. Convert to exponential form. enseryoa 3, Convert (25ab) to simplified radical form, using absolute value when needed. 4. Use Heron's formula to find the area of a triangle with side lengths of 8 in, 10 in, and 12 in. Express your answer using a simplified radical. 10+12
Include all relevant work please. 8. Find the general polynomial function of lowest possible degree with real number coefficients that has -2 and 3i as two of its zeros. Leave in factored form. Also, give the degree of the function you find. 8. P(x)  Degree:
AB 31) Find the eigenvalues and eigenspaces of the matrix-4 0 4 Hint: One way to simplify 6 -2-3 a term of the form a +bi, where a and b are real numbers, is to multiply it by a -bi
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
3. (8 points each) Find the derivative of each function. Show as much work as possible. Do not simplify your answer. 2 (a) f(x) = x-0.5(1 – e2) + 4* + x4 x 2 93 (b) P(t) = + 2-t2 5+5e-3t (c) k(x) = 3 ln(2x +1) VX-5