Numeros Complejos

SUMAS Y RESTAS



(a,b)+(c,d)=(a+c,b+d)

1-

(3+2i)+(1+7i)=(4+9i)

2-

(5+1i)+(6+2i)=(11+3i)

3-

(x+yi)+(2+4i)=(x+2,(y+4)i)

4-

(3-2i) + (4+5i) = (3+4)+(-2+5)i = 7+3i

5-4+1/3i+3/2+2/3i=4+3/2+(1/3+2/3)i=11/2+1i=11/2+i

6-

(5 + 2 i) + ( − 8 + 3 i) − (4 − 2i ) =(5-8-4)+(2+3+2)i=-7+7i



7-

(1+2i)+(4-6i)+(7+xi)=(1+4+7)+(2-6+x)i=12+(-4+x)i

8-

9i+5i=14i9-

(2a+x/yi)+(-3a+2x/yi)=(2a-3a)+(x/y+2x/y)i=-a+(3x/y)i

10-

(12x+8i)+(3y+4i)+(2z+6i)=(12x+3y+2z)+(8+4+6)i=12x+3y+2z+18i



11.-

(5+2i) – (4-2i) = 5+2i-4+2i= 1+4i

12.-

(3-2i) –(5+3i) = 3-2i-5-3i=-2-5i

13.-

(8+4i)-(3-10i)= 8-3+4i+10i= 5+14i

14.-¿+

(5-3i)-(4-7i)= 5-4-3i+7i= 1+4i

15.-

(8-7i)-(15-4i== 8-15-7i+4i= -7-3i

16.-

(4-9i) – (12+2i) = 4-12-9i-2i= -8-11i

17.-

(20-10i) – (11-14i) = 20-11-10i+14i= 9+4i

18.-

(6+5i) – (8+9i) = 6-8+5i-9i= -2-4i

19.-

(7-4i) – (3+8i) = 7-3-4i-8i= 4-12i

20.-

(18+i) – (13+2i) = 18-13+i-2i= 5-iMULTIPLICACIONES

(a+bi)(c+di)= ac+adi+bci+di2

1. (5-2i)(2-3i) = 10-15i-4i+6i2= 10-19i-6(-1)= 116-19i

2. (5-3i)(2+4i) = 10+20i-6i-12i2= 10+14i-12(-1)= 22+14i

3. (7-i)(3-5i)=21-35i-3i+5i2= 21-38i+5(-1)= 16-38i

4. (8+4i)(6-7i)= 48-56i+24i-28i2=48-32i-28(-1)= 76-32i

5. (5(2+3i))(4-5i)=(10+15i)(4-5i)= 40-50i+60i-75i2= 40+10i-75(-1)= 115+10i

6.(2+3i)(9-6i)= 18-12i+27i-18i2= 18+15i-18(-1)= 36+15i

7. (4+2i)(3+2i)= 12+8i+6i+4i2= 12+14i+4(-1)= 8+14i

8. (6x-7i)(5y+8i)= 30xy+48xi-35yi-56i2= 30xy+48xi-35yi+56

9. (12+3i)(a+11i)=12a+132i+3ia+33i2= 12a+132i+3ia-33

10. (7-4i)(8+5i)= 56+35i-32i-20i2= 56+3i-20(-1)= 76+3i

DIVISIONES

a+bi/c+di= (a+bi)(c-di)/(c+di)(c-di) = ac-adi+bci-bdi2/ c2-cdi+cdi+d2= ac+bd+(bc-ad)i/c2+d2

1.3+2i/1-2i= (3+2i)(1+2i)/(1-2i)(1+2i)= 3+6i+2i+4i2/1+2i-2i-4i2= 8i-1/5

2. 3+5i/1-i= (3+5i)(1+i)/(1-i)(1+i)= 3+3i+5i+5i2/ 1-i+i-i2= -2+8i/2= 4i-1

3. 2-ki/k-i= (2-ki)(k+i)/(k-i)(k+i) =...