Download 1.5Precalculus Section 1.5

Precalculus Section 1.5
Perform basic operations with complex numbers
The basic imaginary unit is i.
i=
i2 = -1
A complex number is any number that can be
written in the form a + bi, where a and b are
real numbers a is the real part and bi is the
imaginary part.
Italian mathematician Gerolamo Cardano is the first
known to have conceived complex numbers; he called
them "fictitious", during his attempts to find solutions
to cubic equations in the 16th century.
Complex numbers are used
in physics, electronics.
Computers can create art
called fractals using complex
numbers.
Complex numbers
• Simplify
-2
Simplify
• ( 2 + 3i) + (4 – 5i)
• (9 – 6i) – (3 – 7i)
• (2 + 5i)(6 – i)
• 5 – 2i
4 + 3i
Powers of i
i1 = i
i2 = -1
i3 = -i
i4 = 1
Simplify
i27
i32
assignment
• Page 28
• Problems 1 – 34 not ÷ 3
(40 ec)