write 3i-1/ 1+3i in rectangular form
Answers
Answer:
Rectangular form:
z = -1.2-0.6i
Angle notation (phasor):
z = 1.3416408 ∠ -153°26'6″
Polar form:
z = 1.3416408 × (cos (-153°26'6″) + i sin (-153°26'6″))
Exponential form:
z = 1.3416408 × ei (-0.8524164)
Polar coordinates:
r = |z| = 1.3416408 ... magnitude (modulus, absolute value)
θ = arg z = -2.677945 rad = -153.43495° = -153°26'6″ = -0.8524164π rad ... angle (argument or phase)
Cartesian coordinates:
Cartesian form of imaginary number: z = -1.2-0.6i
Real part: x = Re z = -1.2
Imaginary part: y = Im z = -0.6
Step-by-step explanation:
Calculation steps
Complex number: 2-i
Divide: -3 / the result of step No. 1 = -3 / (2-i) = -3/
2-i
= (-3)*(2+i)/
(2-i)*(2+i)
= -3 * 2 + (-3) * i/
2 * 2 + 2 * i + (-i) * 2 + (-i) * i
= -6-3i/
4+2i-2i-i2
= -6-3i/
4+2i-2i+1
= -6 +i(-3)/
4 + 1 +i(2 - 2)
= -6-3i/
5
= -1.2-0.6i
To divide complex numbers, you must multiply both (numerator and denominator) by the conjugate of the denominator. To find the conjugate of a complex number, you change the sign in imaginary part.
Distribute in both the numerator and denominator to remove the parenthesis and add and simplify. Use rule .
3 × ei : 2.236068 × ei (-0.1475836) = (3 / 2.236068) × ei (-(-0.1475836)) = 1.3416408 × ei (-0.8524164) = -1.2-0.6i
This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i2 = −1 or j2 = −1. The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle). Enter expression with complex numbers like 5*(1+i)(-2-5i)^2
Complex numbers in the angle notation or phasor (polar coordinates r, θ) may you write as rLθ where r is magnitude/amplitude/radius, and θ is the angle (phase) in degrees, for example, 5L65 which is the same as 5*cis(65°).
Example of multiplication of two imaginary numbers in the angle/polar/phasor notation: 10L45 * 3L90.
Why the next complex numbers calculator when we have WolframAlpha? Because Wolfram tool is slow and some features such as step by step are charged premium service.
For use in education (for example, calculations of alternating currents at high school), you need a quick and precise complex number calculator.