Dawnbridge

TI-84 Plus CE field manual for IB Math

HL only · 32 of 41

32

Modulus and argument z∣, argz

HL only

Read the modulus z and principal argument argz of a complex number straight off the calculator (radian mode), then assemble the polar form reiθ.

Goal

Find the modulus z and argument argz of z=5+3i, and hence write z in the form reiθ.

1

Confirm the calculator is in radian mode and complex outputs are enabled: press , make sure RADIAN is highlighted on the angle row and a+bi on the complex row, then back to the home screen.

2

Compute the modulus. Open the complex menu: press , then to land on the CMPLX tab, then for abs(, which inserts the absolute-value bars |▯|. Type and press .

3

Compute the argument the same way: pastes angle(. Type and press .

NORMALFLOATAUTOa+biRADIANMP
5+3i
5.830951895
angle(5+3i)
0.5404195003
Result

z5.83 and argz0.540 rad (both positive, as expected for a first-quadrant number), so z5.83e0.540i.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find the modulus and argument of z=2+5i, and write z in the form reiθ.

  2. 2

    Find the modulus and argument of z=−3+2i, and write z in the form reiθ.

  3. 3

    Find the modulus and argument of z=−14i, and write z in the form reiθ.