3. Simplify the complex number 2+54 + vZe(7) into Cartesian form. 1+3i
4. Find the complex number, n Cartesian form, such that it satisfies the equation (3- V3)(V3 - 3i)s288V3(Y+i)
#1,5,9 and #13,17,21,25 please.
In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
Compute the standard form (a + bi) for the complex number (1 + √ 3i )^10 by first converting to trig form and then applying D’Moivre’s theorem
14 For the complex number z=-3+3i do the following a) Convert to polar form, Polar 2- b) Still in polar form, find z? Polar c) Finally convert z' back to standard form Standard 2' =
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 − sq. root 3i. Write the trigonometric form of the complex number. (Let 0 ≤ θ < 2π.)
5. Consider the complex number z 3i Find the polar form Find z4. Put in non-polar form a. b.
5. Consider the complex number z 3i Find the polar form Find z4. Put in non-polar form a. b.
4. (15 points) Find all the complex solutions of the equation +(V3-3i)(1+2)40. Express the results in Cartesian form (you may express your answer as a function of k, eg. z = eik cos (kπ/2) + isin(kn/2), k = 0, 1, 2, 3, without explicitly evaluating the expression for each k). 2-
4. (15 points) Find all the complex solutions of the equation +(V3-3i)(1+2)40. Express the results in Cartesian form (you may express your answer as a function of k, eg....
3i)16 in polar form: z r(cos 0isin 0) where (1 Write the complex number z and e= The angle should satisfy 0 0 < 2«.