Math 1200: tutorial 5 for oral presentation during tutorial 6 on thursday june 6, 2019 at least 4 of you will be called upon randomly to present your solution orally to one of the questions below during the start of tutorial 6 1. verify iy r - iy (z2) y 2i (z-2) and use for the following (a) identify the graph of |z + 45 in the complex plane (b) identify the graph of (1i)z + (1- i)z = 2. (c) find the equation (in terms of zz coordinates) of the line 2y 4 - (d) identify the graph of iz 2 1+ i 2. explain with a picture (drawing of the unit circle in the complex plane) why there two complex numbers z such that 21 = 1 and that satisfy the equation |2| = |z - i l. find both such complex solutions and express them in euler form z rei and in the usual form za+ bi are 3. solve the quintic equation 25- v3+ i = 0.

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?