HP 33s Scientific Using Complex Numbers in Polar Notation, {G, 9–5, 3 {Gz

2 3 ^‘	.) 
	.) 
3 {Gz	.) 
	)

Enters imaginary part of second complex number as a fraction.

Completes entry of second number and then multiplies the two complex numbers. Result is 11.7333 – i 3.8667.

Evaluate ez −2 , where z = (1 + i ). Use {Gto evaluate z–2; enter –2 as –2 + i 0.

Keys:	Display:	Description:
1 ‘1 ‘		Intermediate result of
0 ‘2 ^{ 		(1 + i )–2
G	.)
	)
{G	.)	Final result is
	) 	0.8776 – i 0.4794.

Using Complex Numbers in Polar Notation

Many applications use real numbers in polar form or polar notation. These forms use pairs of numbers, as do complex numbers, so you can do arithmetic with these numbers by using the complex operations. Since the HP 33s's complex operations work on numbers in rectangular form, convert polar form to rectangular form (using s) before executing the complex operation, then convert the result back to polar form.

a + i b = r (cos θ + i sin θ) = re iθ

= r ∠θ (Polar or phase form)

Operations with Complex Numbers 9–5