Multiplying
Multiplying Imaginary Numbers
It is important that we "take the i's" before doing anything else.
(2√-3)(6√-15)\
= (2i√3)(6i√15)
Use commutative and associative properties to group radicals and non radicals together and multiply.
= (2i)(6i)(√3)(√15)
Now simplify
= 12i2√45
Remember that i2 = -1
= 12(-1)√9 * 5
Simplify
=(-12)(3√5)
Multiply the coefficients
= -36√5
Example #4
Multiply: 3i(13 - 9i)
This one is distributive property.
3i(13 - 9i) = ( ___ )13 - ( ___ )(9i)
Remember i2 = -1
3i(13 - 9i) = ( ___ ) - ( ___ i2)
3i(13 - 9i) = (39i) - (27)( ___ )
Now simplify
3i(13 - 9i) = (39i) + (27)
3i(13 - 9i) = 27 + ___
Example #5
Multiply: (2 + 3i)(3 - i)
This one is binomial multiplication. Some call it FOILfirst, outside, inside, last . I use the distributive property.
Distribute.
(2 + 3i)(3 - i) = ___ (3 - i) + ___ (3 - i)
Distribute the 2 + 3i across the terms in the second set of parentheses. Then, multiply.
(2 + 3i)(3 - i) = 2( 3 - i) + 3i(3 - i)
(2 + 3i)(3 - i) = 6 - ___ + ___ - 3i2
Remember i2 = -1
Now simplify
(2 + 3i)(3 - i) = 6 + 7i + ___
(2 + 3i)(3 - i) = ___ + ___
