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What is the complex conjugate 3i plus 4?
The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number ( 3i + 4 ), which can be expressed as ( 4 + 3i ), the complex conjugate is ( 4 - 3i ).
Is 4 a complex number?
A complex number is denoted by Z=X+iY, where X is the real part and iY is the imanginary part. So the number 4 would be 4+i0 and is the real part of a complex number and so 4 by itself is just a real number, not complex.
Which polynomial will definitely have nonreal zeros?
A polynomial will definitely have nonreal zeros if it has an odd degree and a negative leading coefficient. For example, the polynomial ( f(x) = -x^3 + 2 ) has a degree of 3, which is odd, and the leading coefficient is negative. By the Fundamental Theorem of Algebra, it must have at least one nonreal zero, as it cannot cross the x-axis an odd number of times while remaining entirely above or below it.
What is -4 in standard form as an complex number?
-4=4ei*pi
How many solutions are in x2 plus x plus 4 equals 0?
There are none. For this equation, there is nonreal answer, as the graph of the quadratic does not pass below the x-axis
Is one a real complex pure imaginary or nonreal complex number?
One is a complex number and a real number.
What is the complex conjugate 3i plus 4?
The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number ( 3i + 4 ), which can be expressed as ( 4 + 3i ), the complex conjugate is ( 4 - 3i ).
Is 4 a complex number?
A complex number is denoted by Z=X+iY, where X is the real part and iY is the imanginary part. So the number 4 would be 4+i0 and is the real part of a complex number and so 4 by itself is just a real number, not complex.
Which polynomial will definitely have nonreal zeros?
A polynomial will definitely have nonreal zeros if it has an odd degree and a negative leading coefficient. For example, the polynomial ( f(x) = -x^3 + 2 ) has a degree of 3, which is odd, and the leading coefficient is negative. By the Fundamental Theorem of Algebra, it must have at least one nonreal zero, as it cannot cross the x-axis an odd number of times while remaining entirely above or below it.
What is -4 in standard form as an complex number?
-4=4ei*pi
How many solutions are in x2 plus x plus 4 equals 0?
There are none. For this equation, there is nonreal answer, as the graph of the quadratic does not pass below the x-axis
What is -4-3i divided by 4 plus i?
To divide by a complex number, write it as a fraction and then multiply the numerator and denominator by the complex conjugate of the denominator - this is formed by changing the sign of the imaginary bit of the number; when a complex number (a + bi) is multiplied by its complex conjugate the result is the real number a² + b² which can be divided into the complex number of the numerator: (-4 - 3i) ÷ (4 + i) = (-4 - 3i)/(4 + i) = ( (-4 - 3i)×(4 - i) ) / ( (4 + i)×(4 - i) ) = (-16 + 4i - 12i + 3i²) / (4² + 1²) = (-16 - 8i - 3) / (16 + 1) = (-19 - 8i)/17
What is the multiplicative inverse of 4 plus i?
The multiplicative inverse of a complex number is the reciprocal of that number. To find the multiplicative inverse of 4 + i, we first need to find the conjugate of 4 + i, which is 4 - i. The product of a complex number and its conjugate is always a real number. Therefore, the multiplicative inverse of 4 + i is (4 - i) / ((4 + i)(4 - i)) = (4 - i) / (16 + 1) = (4 - i) / 17.
What is the absolute value of a complex number?
The absolute value of a complex number a+bi is the square root of (a2+b2). For example, the absolute value of 4+9i is the square root of (42 + 92) which is the square root of 97 which is about 9.8489 (The absolute value of a complex number is not complex.)
How do you convert the complex number 4 to polar form?
To convert the complex number 4 to polar form, you first need to represent it in the form a + bi, where a is the real part and b is the imaginary part. In this case, 4 can be written as 4 + 0i. Next, you calculate the magnitude of the complex number using the formula |z| = sqrt(a^2 + b^2), which in this case is |4| = sqrt(4^2 + 0^2) = 4. Finally, you find the argument of the complex number using the formula theta = arctan(b/a), which in this case is theta = arctan(0/4) = arctan(0) = 0. Therefore, the polar form of the complex number 4 is 4(cos(0) + i sin(0)), which simplifies to 4.
The number -4 is what set of numbers?
The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.
What is the multiplicative inverse of 4 i?
The multiplicative inverse of a complex number is found by taking the reciprocal of the number. In this case, the reciprocal of 4i is -1/4i. To find the reciprocal, you divide 1 by the complex number, which results in -1/4i. This is the multiplicative inverse of 4i.
