Questions asked
1. Find the value of; i) $2i^{100} - 5i^{66} + i^7 - 4$ ii) $\frac{i^{16} - 2i + 4i^7}{3i^3 - 4i^2}$ iii) $\frac{j^{-4} + j^9 + j^{16}}{2 - j^5 + j^{10} - j^{15}}$ 2. Simplify the following; i) $(3 + 2i)(4 - i)$ ii) $\frac{3 + 2i}{2 - i}$ iii) $\frac{3 + i}{i(1 - 2i)}$ iv) $\frac{(2 + 3i)(4 - i)^2}{2 + i}$ 3. Express the following complex numbers in trigonometric (polar) forms i) $-3 + 2i$ ii) $-3 - i$ iii) $-2\sqrt{3} - 2i$ iv) $\frac{-1 + i}{(2 - i)i}$ 4. Change the following complex numbers in exponential forms i) $\frac{3\sqrt{3}}{2} + i\frac{3}{2}$ ii) $-3 - 2i$ iii) $\frac{1}{i}$ iv) $\frac{2 - i}{3i(1 - 2i)}$ 5. Given that $z = 4 - 3i$ find; i) $\bar{z}$ ii) $z\bar{z}$ iii) $|z\bar{z}|$ iv) $|z + \bar{z}|$ 6. Plot each complex number and find its modulus a) $4j$ b) $5 + 2j$ c) $\frac{1 - j}{4 - 2j}$ 7. Solve equations; a) $2x^2 + 2x + 1 = 0$ b) $x^5 - 1 = 0$ c) $x^4 + 16 = 0$ 8. Find the values of $a$ and $b$ if $\frac{z_1}{z_2} = z_3$ when $z_1 = -3 + 4j$, $z_2 = a + bj$ and $z_3 = -2 + j$ 9. Solve the equations involving complex numbers a) $\sqrt{2 + j} = 3x - jy$ b) $2(x + jy) = 6 - j3$ c) $(1 + j2)(-2 - j3) = a + jb$ d) $(3x^2 + y^2) + i2xy = 4 + 2i$ e) $\frac{1 + 2j}{1 - j} + \frac{1 - 2j}{1 + 3j} = (x + yj)j$ f) $\frac{jx}{1 + jy} = \frac{3x + j4}{x + 3y}$
Exercise 10.3 2. Find the range in the following sets: a. 2, 3, 7, 20, 6, 8 b. 0, 1, 8, 20, 4, 7.65 c. 85, 91, 132, 76, 35, 47
Karl Marx argues that people would not work if they were not getting paid. Question 7 options: TrueFalse
Find an equation for the plane that passes through the points $(2,0,3)$, $(1,1,1)$ and $(0,3,7)$. State the equation in the form $Ax + By + Cz = D$.
0F? + 4.3301F? - 4.3301F? = 2250 5F? + 2.5F? - 2.5F? = 3897.1 F? + F? + F? = 400
Solve the differential equation.\\ $\frac{dy}{dx} = \frac{1}{7}\sqrt{y}cos^{2}\sqrt{y}$
Which of the following would be an appropriate task to delegate to a UAP or CNA? IM medications Client teaching Care plan Basic hygiene
What is the Konigsberg Bridge Problem? What field of Mathematics is it related to? Why is it so famous?
Draw the carbocation fragment that is associated with the base peak in a mass spectrum of 2,2,3-trimethylbutane.
27. Coqui stock is currently trading at a market price (S) of $72. You do not own the stock, but you have an options strategy in place. You are short a put option on 1 share with a strike price (X) of $65 and have a short call option with a strike price (X) of $89. The premium on the $65 call option was $3. The $89 call option's premium was $2. How would you describe this strategy? * (5 Points) Bullish Bearish Neutral Directional 28. Coqui stock is currently trading at a market price (S) of $72. You do not own the stock, but you have an options strategy in place. You are short a put option on 1 share with a strike price (X) of $65 and have a short call option with a strike price (X) of $89. The premium on the $65 call option was $3. The $89 call option's premium was $2. The call option's premium was $6. What is (are) the stock price(s) where this strategy breaks even? Multiple answers may be correct. Choose all answers that are true. * (5 Points) $55 $60 $70 $84 $92 $94