soluciones_complejos

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MATEMÁTICA II NÚMEROS COMPLEJOS

Soluciones Ejercicios Pág. 4. Tomo I 1. a.

(2 + i)

2

= 4 + 4i + i 2 = 3 + 4i

4

=

b.

(2 + i)

(( 2 + i ) )

2 2

= ( 3 + 4i ) = 9 + 24i + 16i 2 = −7 + 24i 2

c.

1 1( −i ) −i = = = −i i i (−i ) −i 2

d. (1 − 3i )(3 + i ) = 3 + i − 9i − 3i 2 = 6 − 8i

e.

i (2 − i) i 2i − i 2 1 + 2i 1 2 = = = = + i 2 2 + i ( 2 + i )( 2 − i ) 4 − 2i + 2i − i 5 5 5

f. i 3 = i.i 2 = −i 1 − i 3 1 + i (1 + i )( 2 − i ) 2 − i + 2i − i 2 3 + i 3 1 = = = = = + i 2 + i 2 + i ( 2 + i )( 2 − i ) 4 − 2i + 2i − i 2 5 5 5

g. i 3 = −i i 4 = i 2 .i 2 = 1 i 7 = i 3 .i 4 = −i 1 − i + i 3 + 2i 4 + 5i 7 = 1 − i − i + 2 − 5i = 3 − 7i

h. i −12 =

1 1 = =1 12 2 6 i i ( )

1 1 1 − i 3 )( 5 + 3i12 ) = (1 + i ) 8 = 2 + 2i ( 4 4

2. a. 3i = 3π

2

b. 2i 3 = −2i = 2−π

2

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