Polar Form of Complex Number/Examples/12 cis 90

Example of Polar Form of Complex Number

The complex number $\polar {12, 90 \degrees}$ can be expressed in Cartesian form as:

$12 \cis 90 \degrees = 12 i$

and depicted in the complex plane as:

Proof

\(\ds 12 \cis 90 \degrees\)

\(=\)

\(\ds 12 \paren {\cos 90 \degrees + i \sin 90 \degrees}\)

\(\ds \)

\(=\)

\(\ds 12 \times \paren {0 + i \times 1}\)

Cosine of Right Angle and Sine of Right Angle

\(\ds \)

\(=\)

\(\ds 12 i\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Polar Form of Complex Numbers: $84 \ \text {(b)}$