Dawnbridge

TI-Nspire CX II field manual for IB Math

HL only · 33 of 42

33

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

Make sure the document is in Radian mode: press 7: Settings & Status2: Document Settings and confirm Angle = Radian.

2

Compute the modulus. From the Scratchpad calculator, paste the magnitude tool: (Number) (Complex Number Tools) (Magnitude). The Nspire writes the modulus bars |▯|; inside them type → highlight i , then for the decimal.

3

Compute the argument: (Polar Angle) pastes angle(. Type  i  , then . (Plain would return the exact tan−1(3/5) form.)

Scratchpad
RAD
5+3i
5.83095
angle(5+3i)
0.540420
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.