Dawnbridge

TI-Nspire CX II field manual for IB Math

HL only · 35 of 45

35

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 & Status → 2: 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

​∣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. 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=−1−4i, and write ​z​ in the form ​reiθ.