Graphing in the Complex Plane
Read this topicExplanations 5
- The Complex Plane and Vector Analogy In this explanation, we'll extend imaginary numbers to the set of complex numbers (not as "complex" as they seem!) and we'll look at the geo…
By Eric Zhang, Yousuf Soliman, Expii Team
- What if we wanted to graph the number zzz, where z=z=z= 555+++3i3i3i Well zzz is a complex number, so we cannot graph it on the regular Cartesian plane. We must graph it on the …
By Evan Tong
- Here is an awesome video: The original page is at BetterExplained.com.
By Ray Li, Victor Wang
- Let x,y∈Rx,y\in\mathbb{R}x,y∈R. (R=\mathbb{R}=R= the set all real numbers). Then, z=x+iyz=x+iyz=x+iy is a complex number. Now, how do we graphically represent this? The answer l…
By Neelarnab Raha
- The Complex Plane We've now learned that Complex Numbers take the form of z=a+biz=a+biz=a+bi. Our next step is to learn how they appear on the complex plane. The complex plane i…
By Jonathan Heller, Caroline K, Victor Wang
Problems 9
- Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are 1+2i1+2i1+2i, −2+i-2+i−2+i, and −1−2i-1-2i−1−2i. Find the real part of the fo…
- What is the graphical interpretation (in the complex plane) of a complex conjugate?
- What is the area of the polygon in the complex plane with vertices at 1,i,i2,i31,i,i^2,i^31,i,i2,i3?
- Let z,wz,wz,w be complex numbers with magnitudes ∣z∣=1|z| = 1∣z∣=1 and ∣w∣=4|w| = 4∣w∣=4. What is the largest possible value of the magnitude ∣z−w∣?|z-w|?∣z−w∣?
- Let z,wz,wz,w be complex numbers with magnitudes ∣z∣=1|z| = 1∣z∣=1 and ∣w∣=4|w| = 4∣w∣=4. What is the largest possible value of ∣(3+4i)z−w∣|(3+4i)z-w|∣(3+4i)z−w∣?
- What is the smallest possible value of ∣(2+3i)−(a+bi)(1+i)∣|(2+3i) - (a+bi)(1+i)|∣(2+3i)−(a+bi)(1+i)∣ for integers a,ba,ba,b?
- How many points z=a+biz = a+biz=a+bi in the complex plane, with a,ba,ba,b integers, satisfy ∣z∣=1?|z| = 1?∣z∣=1?
- Let AAA be the point 2+3i2+3i2+3i in the complex plane, let OOO be the origin 0=0+0i,0 = 0+0i,0=0+0i, and let BBB be the point 2+3ii.\frac{2+3i}{i}.i2+3i. What is the angle mea…
- In the complex plane, the number line has two axes: one real, one imaginary. The real line is as normal, and the imaginary line is exactly like the real line, except vertical di…