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To take the square root of a complex number:* Write the original complex number in polar notation (absolute value and angle).
* For the square root, the angle will be half the angle. The absolute value will be the square root of that of the original number.
* There is a second square root: the same as above, but add 180 degrees (or pi, if using radians) to the angle.
* If you wish, you can convert the result(s) back to rectangular coordinates, i.e., real number + imaginary number.
Most scientific calculators have functions to convert from rectangular to polar and vice versa.
For 18 + 24i,r^2 = 18^2 + 24^2 = 900 => r = 30and alpha = atan(24/18) => beta = 0.9273 radians, approx
So, for the solution s = sqrt(r) = sqrt(30)
and beta = alpha/2 = 0.4636 radians.
Then sqrt(18 + 24i) = s*cos(beta) + s*sin(beta)*i
= 4.8990 + 2.4495*i
The second square root is - 4.8990 - 2.4495*i
If you represent the number as a magnitude and an angle, then the square root of that number will be the positive square root of the magnitude, and then divide the angle by 2. To get the other square root, add 180° to the angle (or pi radians) to the angle of the answer.
So your number just happens to form a scale of a 3-4-5 right triangle, so it is sqrt(6*(3 + 4i)), or sqrt(30*(0.6 + 0.8i)). The magnitude is 30, and the magnitude of the square root is sqrt(30).
The angle is approx 53°. The angle of the square root is approx 26.5°, and the other angle is 206.5°
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What complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
A number written in the form a plus bi is called a number?
complex
What is the complex conjugate of the following complex number 7 plus 5i?
The conjugate is 7-5i
What is the conjugate of the complex number 9 plus 5i?
9-5i
What is a number that can be written in the form a plus bi where a and b are real numbers?
A number of the form (a + bi) is a complex number.
How do you write 11 plus 8i as a complex number?
It is just 11+8i.
A complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
What complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
How do you write complex numbers in the form a plus bi?
A complex number comes in two parts: a real part and an imaginary part. If the value of the real part is a and the value of the imaginary part is b, the number is written as a + bi.
What is a non real complex number?
Complex numbers are written in the form (a+bi), where i is the square root of -1.A real number does not have any reference to i in it.A non real complex number is going to be a complex number with a non-zero value for b, so any number that requires you to write the number i is going to be an answer to your question.2+2i for example. (2 plus 2 times i)
A number written in the form a plus bi is called a number?
complex
What is a number written in the form a plus bi is called a what number?
It is called a complex number.
What is the complex conjugate of the following complex number 7 plus 5i?
The conjugate is 7-5i
What is the conjugate of the complex number 9 plus 5i?
9-5i
What is the magnitude of the complex number 8 plus 2i?
8.2462 (rounded)
What is a number of the form a plus bi where a is the real part and b is the imaginary part?
a complex number
What is a number that can be written in the form a plus bi where a and b are real numbers?
A number of the form (a + bi) is a complex number.
