Multiply the following complex numbers:
\left(A_REP\right) \cdot \left(B_REP\right)
The first number is plotted in blue and the second number is plotted in green. Your current answer will be plotted in orange.
10Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles.
The first number, A_REP,
has angle A_ANGLE_REP
and radius A_RADIUS_REP.
The second number, B_REP,
has angle B_ANGLE_REP
and radius B_RADIUS_REP.
The radius of the result will be
A_RADIUS_REP \cdot B_RADIUS_REP = ANSWER_RADIUS_REP.
The sum of the angles is A_ANGLE_REP + B_ANGLE_REP = INTERMEDIATE_ANGLE_REP.
The angle INTERMEDIATE_ANGLE_REP is more than 2 \pi.
A complex number goes a full circle if its angle is increased by 2 \pi, so it goes back to itself.
Because of that, angles of complex numbers are convenient to keep between 0 and 2 \pi.
INTERMEDIATE_ANGLE_REP - 2 \pi = ANSWER_ANGLE_REP
The angle of the result is A_ANGLE_REP + B_ANGLE_REP = ANSWER_ANGLE_REP.
The radius of the result is ANSWER_RADIUS_REP
and the angle of the result is ANSWER_ANGLE_REP.
Divide the following complex numbers:
\Large{\dfrac{A_REP}{B_REP}}
\dfrac{A_REP}{B_REP}
The dividend is plotted in blue and the divisor is plotted in green. Your current answer will be plotted in orange.
10Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles.
The dividend, A_REP,
has angle A_ANGLE_REP
and radius A_RADIUS_REP.
The divisor, B_REP,
has angle B_ANGLE_REP
and radius B_RADIUS_REP.
The radius of the result will be
\dfrac{A_RADIUS_REP}{B_RADIUS_REP} = ANSWER_RADIUS_REP.
The difference of the angles is
A_ANGLE_REP - B_ANGLE_REP = INTERMEDIATE_ANGLE_REP.
The angle INTERMEDIATE_ANGLE_REP is negative.
A complex number goes a full circle if its angle is increased by 2 \pi, so it goes back to itself.
Because of that, angles of complex numbers are convenient to keep between 0 and 2 \pi.
INTERMEDIATE_ANGLE_REP + 2 \pi = ANSWER_ANGLE_REP
The angle of the result is A_ANGLE_REP - B_ANGLE_REP = ANSWER_ANGLE_REP.
The radius of the result is ANSWER_RADIUS_REP
and the angle of the result is ANSWER_ANGLE_REP.