Trident Help

Natural Scientific 991 manual · Chapter 8 of 18

Complex numbers

Arithmetic with i, real and imaginary parts, conjugate, argument and rectangular/polar conversion.

8.1Open the Complex app and type i#

Press MENU then 2 to open the Complex app. The CMPLX indicator appears. In this app the ENG key types the imaginary unit i. Complex answers appear as a+bi.

Example 8.1

Square a complex number

  1. Open Complex. Type (1 + 2i)².

    MENU2(1+2ENG)x²

  2. Equals.

    =
Result of the example "Square a complex number" The display shows: (1+2i)² / -3+4i.
You should see-3+4i
Example 8.2

Multiply complex numbers

  1. (3 + 4i)(1 − 2i).

    MENU2(3+4ENG)×(1−2ENG)=
Result of the example "Multiply complex numbers" The display shows: (3+4i)×(1−2i) / 11-2i.
You should see11-2i
Example 8.3

The root of a negative number

  1. √-4 gives 2i in this app.

    MENU2√(−)4=
Result of the example "The root of a negative number" The display shows: √(-4) / 2i.
You should see2i

8.2Argument, conjugate, real and imaginary parts#

Press OPTN in the Complex app for the list below. Each one types a function you complete with a complex number and a closing bracket.

OPTN numberItemMeaning
1ArgumentThe angle of the number in the complex plane.
2ConjugateChanges the sign of the imaginary part.
3Real PartThe a in a+bi.
4Imaginary PartThe b in a+bi.
5►r∠θShows the previous number in polar form.
6►a+biShows the previous number in rectangular form.
7iTypes i.
Example 8.4

Argument of 3 + 4i

  1. OPTN 1, then 3 + 4i and a bracket.

    MENU2OPTN13+4ENG)=
Result of the example "Argument of 3 + 4i" The display shows: arg(3+4i) / 53.13010235.
You should see53.13010235
Example 8.5

Conjugate of 3 + 4i

  1. OPTN 2.

    MENU2OPTN23+4ENG)=
Result of the example "Conjugate of 3 + 4i" The display shows: Conjg(3+4i) / 3-4i.
You should see3-4i
Example 8.6

Real part

  1. OPTN 3.

    MENU2OPTN33+4ENG)=
Result of the example "Real part" The display shows: ReP(3+4i) / 3.
You should see3
Example 8.7

Imaginary part

  1. OPTN 4.

    MENU2OPTN43+4ENG)=
Result of the example "Imaginary part" The display shows: ImP(3+4i) / 4.
You should see4
The Complex OPTN menu The display shows: 1:Argument / 2:Conjugate / 3:Real Part / 4:Imaginary Part.
The Complex OPTN menu

8.3Convert to polar form#

You can ask for polar form for a single answer with ►r∠θ from OPTN 5, or set polar as the default: SETUP, 5 (Complex), 2 (r∠θ). To type a polar number use SHIFT∠(−) (∠) between the modulus and the angle.

Example 8.8

Convert 3 + 4i to polar

  1. Type 3 + 4i, then OPTN 5.

    MENU23+4ENGOPTN5=
Result of the example "Convert 3 + 4i to polar" The display shows: 3+4i►r∠θ / 5∠53.13010235.
You should see5∠53.13010235
Example 8.9

Polar as the default

  1. SETUP, 5, 2. Then 1 + i.

    MENU2SHIFTSETUPMENU521+ENG=
Result of the example "Polar as the default" The display shows: 1+i / √2∠45.
You should see√2∠45
Example 8.10

Type a polar number

  1. 3 ∠ 30, in degrees.

    MENU23SHIFT∠(−)30=
Result of the example "Type a polar number" The display shows: 3∠30 / 3√3/2+3/2i.
You should see3√3/2+3/2i
a+bi=r∠θ,r=a2+b2,θ=tan⁡−1baa+bi = r\angle\theta,\quad r=\sqrt{a^2+b^2},\quad \theta=\tan^{-1}\frac{b}{a}
Rectangular and polar form

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