Review your knowledge of the complex number features: absolute value and angle. Convert between them and the rectangular representation of a number.
Log in 🤔 ᴄᴏᴅᴇᴅ ɢᴇɴɪᴜȿ 😎 7 years agoPosted 7 years ago. Direct link to 🤔 ᴄᴏᴅᴇᴅ ɢᴇɴɪᴜȿ 😎's post “I found a really easy way...” I found a really easy way to solve the problems in the earlier exercise! My question is, is there anything wrong with the way that I solve this? Is there a problem that I could run into, using this? • (17 votes) ZeroFK 7 years agoPosted 7 years ago. Direct link to ZeroFK's post “That looks correct. You ...” That looks correct. You have found a theorem - can you prove it? (11 votes) marialagakos 4 years agoPosted 4 years ago. Direct link to marialagakos's post “Is there a way to know wh...” Is there a way to know when to add or substract 180degrees or pi? For example, if the a is negative and the b is positive, is there a way to know exactly whether or not to add or subtract? And this for three other cases (both positive, both negative, a positive and b negative)? • (12 votes) matthewmorris628 4 years agoPosted 4 years ago. Direct link to matthewmorris628's post “I believe I have found th...” I believe I have found the answer to when to add/ subtract 180degrees/pi. I have tested my theory with numerous examples and it has proven to work: Hope this is helpful! (14 votes) nmj834481993 7 years agoPosted 7 years ago. Direct link to nmj834481993's post “Does anyone know how to t...” Does anyone know how to tell which quadrant the question was asking? e.g. Express • (7 votes) Sarah 7 years agoPosted 7 years ago. Direct link to Sarah's post “The 180 and -180 degree c...” The 180 and -180 degree clarifications are there to ensure that you don't input wild values like 7928 degrees--stay within the boundaries, and you're fine. As for the quadrants, it helps me to sketch the point. However, if you feel like memorizing, remember that a positive a and a negative b will always be in the fourth quadrant, and you can figure out the other three :) (7 votes) anahope03 4 years agoPosted 4 years ago. Direct link to anahope03's post “In some of the questions ...” In some of the questions on the complex numbers from absolute value and angle practice, it instructs to list answers in exact terms. How is this obtained from the rcos(θ) + rsin(θ) * i formula? • (7 votes) joinmathism1 a year agoPosted a year ago. Direct link to joinmathism1's post “Some values of sine and c...” Some values of sine and cosine have values that you can figure out by hand such as trigonometric values in a 30-60-90 triangle or 45-45-90 triangles and other trig values you can derive from these triangles. (1 vote) dsumner602.DS 4 years agoPosted 4 years ago. Direct link to dsumner602.DS's post “when i put in 2cos(30) in...” when i put in 2cos(30) into my calculator i get 1.732050808 and it was telling me thats wrong. It took me a while to figure out that if i square that number i get the square root of three. and thats the format that it accepts it as. i guess my question is that that what everyone else is doing is squaring there answere to see if it comes to a a natural number to determine what format to put it in? • (6 votes) Jimmy 3 months agoPosted 3 months ago. Direct link to Jimmy's post “If the exersize doesn't t...” If the exersize doesn't tell you to round, it will probably not be a decimal. You should also memorize all the special triangle formulas. (1 vote) at155204 7 years agoPosted 7 years ago. Direct link to at155204's post “hi, i want to ask one que...” hi, i want to ask one question. How to solve this type of question? • (3 votes) andrewp18 7 years agoPosted 7 years ago. Direct link to andrewp18's post “First we find all side le...” First we find all side lengths of the triangle. Let 𝑝 = 8 – 𝑖 and 𝑞 = 12 + 6𝑖. Then: (4 votes) Wilson Cheung 4 years agoPosted 4 years ago. Direct link to Wilson Cheung's post “Why do we need to add 180...” Why do we need to add 180 degrees in Example 2: Quadrant || • (3 votes) El 4 years agoPosted 4 years ago. Direct link to El's post “Think of it this way: the...” Think of it this way: the angle is how far the modulus/absolute value is from the positive side of the real number axis. When the modulus is in Quadrant 1, like in the example before Example 2, it is only 53 degrees away from it. Whereas in Example 2, the modulus is an additional 180 degrees to the left because it is in Quadrant 2, which is why we need to add 180 degrees. Does that make sense? (4 votes) Akshat 8 years agoPosted 8 years ago. Direct link to Akshat's post “Can someone explain how t...” Can someone explain how to find inverse of trigo functions • (2 votes) Luis F. Vélez 8 years agoPosted 8 years ago. Direct link to Luis F. Vélez's post “You have to use a calcula...” You have to use a calculator for this particular kind of operation, usually labeled as arc then trig function (e.g. arccos(x)) or the trig function raised to the negative one power (e.g. sin^-1(x)). (3 votes) Br Paul 4 years agoPosted 4 years ago. Direct link to Br Paul's post “Usually I do fine in math...” Usually I do fine in math, but finding the rectangular form in exact terms (as in the form a+b i where a = 5 times the square root of 3 and b = the square root of 7, for example) is really stumping me. So far, I have only got one problem right, and that was through trial and error. How exactly am I supposed to find the rectangular form in exact terms? • (3 votes) loumast17 4 years agoPosted 4 years ago. Direct link to loumast17's post “So you need your unit cir...” So you need your unit circle memorized or written down. You will always be given the absolute value of the complex number (the length) and angle the line makes with the positive x axis. Let's call the length r and angle t. The first step is easy, you take those two numbers and plug them into this. r*cos(t) + r*sin(t)*i From there you solve the trig functions, which is where you ned your unit circle. Does that help? (2 votes) Pradeep Kumar 4 years agoPosted 4 years ago. Direct link to Pradeep Kumar's post “how do we know when to su...” how do we know when to subtract 180 degrees from theta and when i should add 180 degrees to theta? Please help! • (3 votes) sidmahapatra13 a year agoPosted a year ago. Direct link to sidmahapatra13's post “If the angle theta lies i...” If the angle theta lies in quadrant 2 you must add 180 and quadrant 3 substract 180 (1 vote)Want to join the conversation?
Take the cos of the angle and multiply it by the magnitude to get the x value (rounding it to the nearest thousandth) and use sin for the y value but do the same thing.
Example:A complex number z₁ has a magnitude |z₁| = 20 and angle θ₁ = 281°Express z₁ in rectangular form, as z₁ = a + bi.Round a and b to the nearest thousandth.a = cos(θ₁) × |z₁|b = sin(θ₁) × |z₁|
Hint: try drawing it on a standard Cartesian plane and using trigonometry for the proof. Represent your complex number as a line starting at the origin, at an angle of theta, and with length |z|.
If your point lands in Q1= no adding or subtracting, Q2= add 180 or pi, Q3= subtract 180 or pi, and Q4= no adding or subtracting.
θ between −180 and 180 degree. I finished the trig, most went well but I'm always confused with the range they set up and always get the wrong answer.
This is how I understood the phrase "Express theta between -180 and 180 degree": I draw a unit circle, then go from 0 degree (which is the right side of the x-axis) to 180 degree (the left side of x-axis); then I do the same from 0 degree to -180 degree (so it is a clockwise rotation of 180 degree to the left side of x-axis). As the result I don't know which area/quadrants the question was asking because both 180 and -180 degree are on the same line (the left side of the x-axis).
Question:
The points P and Q in an Argand diagram represent the complex number 8-i and 12+6i respectively and O is the origin. Show that the triangle OPQ is isosceles and calculate the size of angle OPQ correct to the nearest degree.
𝑃𝑂 = |𝑝| = √65
𝑄𝑂 = |𝑞| = 6√5
𝑃𝑄 = |𝑝 – 𝑞| = √65
Thus ∆𝑃𝑄𝑂 is isosceles.
Finding ∠𝑂𝑃𝑄 is easy with the Law of Cosines:
180 = 65 + 65 – 2 • 65²cos 𝑃
This gives:
cos 𝑃 = -25/65²
Or:
cos 𝑃 = -1/169
Taking the arccosine of both sides gives 𝑃 ≈ 90.34˚ which is simply 90˚ when rounded to the nearest degree.
Comment if you have questions!
