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Q: What is the sum of 12 5i and 3 4i?
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Plot the number in a complex plane -1-3i?

2


What is the reciprocal of 3 plus 5i?

1/(3+5i)=(3-5i)/((3+5i)(3-5i))=(3-5i)/(9+25)=(3-5i)/34


What is the sum of the serious if n equals 5 and ai equals 4i plus 3?

I cannot take this question seriously! The sum is 75.


How do you find the additive inverse of a complex number?

You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).You take the additive invers of the real and of the imaginary part. For instance, the additive inverse of: (3 - 5i) is (-3 + 5i).


Complex conjugate of 5i?

0 + 5i Its complex conjugate is 0 - 5i


What are 10 complex numbers with the absolute value of 5?

Use the Pythagorean theorem. 5, -5, 5i, and -5i will work, as well as any combination of a real and imaginary number such that (real part) squared + (imaginary part) squared = 25, for example, 4 + 3i, 3 + 4i, 4 - 3i, etc.


What is the conjugate of 3 plus 4i?

When finding the conjugate of a binomial, you just reverse the sign. So the conjugate of 3+4i is 3-4i.


What are the cube roots of 1000i?

5√3 + 5i, -5√3 + 5i, -10i


Convert to polar form and then divide Express your answer in polar form 5 sqare root of 3 -5i divided by 4 plus 4isquare root of 3?

(5√3 - 5i)/(4 + 4i√3)Let's try to represent the given complex numbers in the polar form.z = |z|(cos θ + i sin θ)Let z1 = 5√3 - 5i in the form a + bi, wherea1 = |z1|cos θ1 andb1 = |z1| sin θ1so that|z1| = √(a12 + b12) = √[(5√3)2 + (- 5)2] = √(75 + 25) = √100 = 10cos θ = a1/|z1|= 5√3/10 = √3/2 andsin θ = b1/|z1|= -5/10 = -1/2So that,z1=5√3 - 5=|z1|(cos θ1 + i sin θ1) =10(√3/2 - i1/2), where θ1 = 330 degreesLet z2 = 4 + 4√3i|z2|=√(42 + (4√3)2) = √(16 + 48) = √64= 8cos θ2 = 4/8 = 1/2sin θ2 = (4√3)/8 = √3/2So that,z2 = 4 + 4√3 = |z2|(cos θ2 + i sin θ2) = 8(1/2 + √3/2i), where θ2 = 60 degreesNow let's divide.Recall the Euler formula: z = |z|eiθ, wher eiθ = (cos θ + i sin θ)z1/z2 = |z1|eiθ1/|z2|eiθ2 = (|z|/|z|)ei(θ1 - θ2) = (|z|/|z|)[cos (θ1 - θ2) + i sin (θ1 - θ2)]z1/z2 = (10/8)[cos (330 - 60) + i sin (330 - 60)] = (5/2)( cos 270 + i sin 270) = (5/4)(0 - i )Let's check:(5√3 - 5i)/(4 + 4i√3)= (5√3 - 5i)(4 - 4i√3)/(4 + 4i√3)(4 - 4i√3)= (20√3 - 60i - 20i + 20i2√3)/(16 - 48i2)= (20√3 - 80i - 20√3)/(16 + 48)= -80i/64= -5i/4= 0 - 5i/4= (5/4)(0 - i)


What is the sum of -3 and -12?

9


What is the multiplicative inverse of 3-4i divided by 5 plus 2i?

The multiplicative inverse of a number a is a number b such that axb=1 If we look at (3-4i)/(5+2i), we see that we can multiply that by its reciprocal and the product is one. So (5+2i)/(3-4i) is the multiplicative inverse of (3-4i)/(5+2i)


What is the product of these complex numbers (3-4i)(1-i)?

(3-4i)(1-i) = (3x1) + (3 x -i) + (-4i x 1) + ( -4i x -i) = 3 - 3i -4i -4 = -1 - 7i