Imaginary & Complex Numbers EQ : Why do imaginary numbers exists and how do you add/subtract/multiply/divide imaginary numbers?

Why do we need imaginary numbers?  Allow us to make calculations that otherwise would not be possible (ex. Electric circuits)

i 2=

Powers of ii1i1 i2i2 i3i3 i4i4 i5i5 i6i6 i7i7 i7i7... Simplified form i -i 1 i -i 1...

How to re-write radicals using “i”  Re-write as multiple of -1 Separate radicals Substitute

Ex 1) Re-write using the number “i”

Ex 2) Simplify Change to “i” form first!!! Multiply Substitute i 2 = -1 Factor Multiply coefficients

You Try! – Simplify each imaginary expression  a.  b.  c.

COMPLEX NUMBERS Real #s Ex) 2, -5, 1.3 Imaginary #s Ex) 5 i Rational Irrational Integers etc. a+bi

Ex 3) Simplify

Ex 4)

Ex 5)

Conjugate  The opposite operation between two terms.  Ex) 5 + 2i conjugate: 5 – 2i  Imaginary numbers may never be in the denominator  To eliminate them, multiply the numerator & the denominator by the conjugate

Ex 6) Simplify by rationalizing the denominator Multiply top & bottom by conjugate Substitute i 2 = -1

Ex 7) Simplify by rationalizing the denominator

 Calculator: To use the imaginary number press 2 nd,

Exit Ticket: Use the calculator to simplify:  1.  2.

Homework