Find the prodect of 3 - 7t and 2 + st. (2) Write in the form a + bt (3 + i)/(10

Question

Find the prodect of 3 - 7t and 2 + st. (2) Write in the form a + bt (3 + i)/(10 - 2i) (3) For each complex number, write it in polar form. (a) 1 - 3t (b) -5 + 5t (c) I (4) Write in the form a + bi; ( 3 - i)^2 (5) Write in the form a + bi; 1/(5 - 3t)^10 (6) Find all solutions of the equation z^4 = 1. (7) Find the square root(s) of 2 - 1t. (8) Find the eighth root(s) of i. (That is, find 1^1/5) (9) Let z_1 and z_2 be complex numbers that live on the unit circle. Explain why z_1 z_2 is still on the unit circle. (10) Let z = r(cos theta + i sin theta). Use geometry to explain why z^n = r^n(cos(ntheta) + i sin(ntheta))

Explanation / Answer

16
a) i(pi/2)
b) 0.804 - 0.463 i
c) 0.2078 i
d) 0.220 - 0.975 i
e)0.540 + 0.841 i
f) -1.371 + 2.167 i

17) i^(1/i) = (e^(i*pi/2))^1/i=e^(pi/2)=4.8104 this is not a general solution
for general solutiopn pi/2 can be replaced by pi/2 + 2pi*k , k=0,1,2,....

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