Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Do you really want to delete this prezi?
Neither you, nor the coeditors you shared it with will be able to recover it again.
Make your likes visible on Facebook?
You can change this under Settings & Account at any time.
Transcript of Complex Numbers
So i=√-1 i²=-1 √-9 -5=0
3i-5=0 You cannot combine imaginary and real numbers. Multiply the complex number by its complex conjugate.
6-4i Division Using Complex Conjugates To divide two complex numbers, multiply both complex numbers by the bottom number's complex conjugate. 8-7i (1+2i)
1-2i (1+2i) 1) 2) Use the distributive property on both top and bottom. 8+16i-7i-14i²
1-2i+2i-4i² Remember that i²=-1, so you substitute in -1 for every i². 3) 8+9i-14(-1)
1-4(-1) 4) This becomes +14. This becomes +4. 22+9i
5 This is your final answer. 5i
(2+3i)² Example: Combine like terms. The normal rules of addition and subtraction apply. When subtracting, remember to distribute the negative. Example: (7+6i)+(3+12i) 1) 1) 2) (6-4i)(6+4i) Use the Distributive Property. 3) 36-24i+24i-16i² Remember i²=-1 4) 36-16(-1) 5) 52 2) Combine like terms. (7+3)+(6i+12i) Simplify. 3) 10+18i This is your final answer. 1) (13i)-(14-7i) Distribute the negative. 2) 13i-14+7i Combine like terms. 3) -14+20i Your final answer is in standard form. Example: 3
5 i + ( ) - 5
6 - ( ) i Sometimes when you use the quadratic formula, you end up with a negative under the radical. If you factor out the i, you can give your answer in standard form. Example: x²-2x+2=0 Set up the problem using the quadratic formula. x=2±√(-2)²-(4(1)(2))
2(1) Simplify whatever possible. x=2±√-4
2 Think of √-4 as two terms. x=2±(√4)(√-1)
2 Remember that √-1=i. x=2±2i
2 = x=1±i This is your final answer. 1) 2) 3) 4) 5) Example: 9x²-6x+37=0 Using your calculator, you can enter the number i. Shift and will get you i. . You can also change your calculator's mode from real to imaginary. If you want an answer in decimal form, use parentheses around the expression. Khan Academy has a series of videos with step-by-step explanations of the number i and operations using complex numbers. You can access Khan Academy without an account at www.khanacademy.org Multiplication Example: (6-2i)(2-3i) Remember to use the distributive property. When am I ever going to use this? According to Technology Integration Partnerships, engineers and physicists both use imaginary numbers to measure electrical currents and the flow of liquids. Z=V+Ii Impedance Voltage Current