Casio fx-CG50 field manual for IB Math
Modulus and argument ∣z∣, argz
Read the modulus ∣z∣ and principal argument argz of a complex number straight off the calculator (radian mode), then assemble the polar form reiθ.
Find the modulus ∣z∣ and argument argz of z=5+3i, and hence write z in the form reiθ.
From the MAIN MENU, open Run-Matrix (icon 1). Press and confirm Angle = Rad and Complex Mode = a+bi; press to return.
Open the complex tools: press (COMPLEX). The soft-menu strip now shows i, Abs, Arg and Conjg; ReP and ImP sit on the second strip under (▶).
Compute the modulus: press (Abs) to paste Abs(, then type i and press . Insert the imaginary unit with (i). Press if the Casio answers with the exact √34 rather than a decimal.
Compute the argument: the menu closes when you press , so reopen it with (COMPLEX), then press (Arg) to paste Arg(, type i and press . Press once if the Casio shows the symbolic tan−1(3/5) form rather than the decimal.
∣z∣≈5.83 and argz≈0.540 rad (both positive, as expected for a first-quadrant number), so z≈5.83e0.540i.
Your turn
Work each one on your calculator, then check the answer.
- 1
Find the modulus and argument of z=2+5i, and write z in the form reiθ.
- 2
Find the modulus and argument of z=−3+2i, and write z in the form reiθ.
- 3
Find the modulus and argument of z=−1−4i, and write z in the form reiθ.