To multiply complex numbers, we can use the distributive property and remember that (i^2 = -1).
( (2+i)(3-i) )( = 2 \cdot 3 - 2i + 3i - i(-i) )( = 6 - 2i + 3i + i^2 )( = 6 + i + 1 )( = 7 + i )
( (5+6i)(-2+3i) )( = 5(-2) + 5(3i) + 6i(-2) + 6i(3i) )( = -10 + 15i - 12i + 18i^2 )( = -10 + 3i - 12i - 18 )( = -28 - 9i )
Therefore, ( (2+i)(3-i) = 7 + i ) and ( (5+6i)(-2+3i) = -28 - 9i )
To multiply complex numbers, we can use the distributive property and remember that (i^2 = -1).
( (2+i)(3-i) )
( = 2 \cdot 3 - 2i + 3i - i(-i) )
( = 6 - 2i + 3i + i^2 )
( = 6 + i + 1 )
( = 7 + i )
( (5+6i)(-2+3i) )
( = 5(-2) + 5(3i) + 6i(-2) + 6i(3i) )
( = -10 + 15i - 12i + 18i^2 )
( = -10 + 3i - 12i - 18 )
( = -28 - 9i )
Therefore, ( (2+i)(3-i) = 7 + i ) and ( (5+6i)(-2+3i) = -28 - 9i )