Complex numbers

7.1Turn on complex numbers#

In REAL mode, the square root of a negative number is an error. To work with complex numbers set the third line of MODE to a+bi (answers like 3+4i) or r∠θ (answers as a length and angle). Then CPX appears on the screen.

Example 7.1

Square root of a negative number

1. Switch to a+bi, clear, then take the root of -4.

   mode▼▼▼▶enterclear2nd√x²(−)4enter

Example 7.2

Error in real mode

1. In the default REAL mode the same root is an error.

   2nd√x²(−)4enter

See also Complex numbers

7.2Use i, conj, real, imag and angle#

The CPX tab of the MATH menu (math, ▶, ▶) has i (item 1), conj( (2), real( (3), imag( (4) and angle( (5). conj changes the sign of the imaginary part, real and imag pick out the two parts, and angle gives the angle of the number.

Example 7.3

Type a complex number

1. Press the i item from the CPX tab.

   mode▼▼▼▶enterclear3+4math▶▶1enter

Example 7.4

Multiply by the conjugate

1. (1+i)(1−i) is the real number 2.

   mode▼▼▼▶enterclear(1+math▶▶1)×(1−math▶▶1)enter

Example 7.5

Conjugate

1. Pick conj( and type 3+4i.

   mode▼▼▼▶enterclearmath▶▶23+4math▶▶1)enter

Example 7.6

Imaginary part

1. Pick imag( and type 3+4i.

   mode▼▼▼▶enterclearmath▶▶43+4math▶▶1)enter

Example 7.7

Angle of a complex number

1. Pick angle( and type 3+4i.

   mode▼▼▼▶enterclearmath▶▶53+4math▶▶1)enter

7.3Show complex answers in polar form#

Example 7.8

Polar answer

1. Choose r∠θ on the complex line of MODE. The answer is a length and an angle.

   mode▼▼▼▶▶enterclear3+4math▶▶1enter