Evaluate the quotient (5 + i)/(1 + 3i)

Write 2 (1 + i) – 3(2-3i) in the form of a +bi

 

next we can write 

Write (2-2i)^8 in the standard form a+bi

(z+1)/(z-1) = ki show that z*zbar =1

z= ((3+4i)(12-5i))/(2+i) a. |z| ? b. Re (z) and Im (z)?

Expanding the numerator







 

        

Write the expression in the form a + bi, where a and b are real numbers. sqrt(-1)/( sqrt(-81)sqrt(-36))

How do you solve for m and n in the equation: 5+15i=2m+3ni?

Real parts:
5=2m
m=5/2
Imaginary parts:
15i=3ni
n=5

Simplify: (3i)(i)(8-8i)

(3i)(i)(8-8i)=
3*i^2*(8-8i)=
-3(8-8i)=
-24+24i

find value of x and y if, x/(1+i)+y/(2-i)=2+4i

leads to


Real:

Imaginary:

when solved we get

14-i to the sixth power divided by i

then we can write
 at  and multiply the result by -i
this yields:
-3172148-6956235i

What does -i equal?

Solution:
It is a power of the imaginary unit i:
i^3=-i

Please help me solve this equation. X^2=-7

Using the square root property:
 or 

Write z=2-2i in trigonometric form.

Find the absolute value of 2+4i.

Simplify: (4+4i)/(2-9i)

Multiplying my complex conjugates and simplifying the denominator we get:



then we get...

Simplify: sqrt(-27x^5)

how do you simplify (5-2i)/(-4+i) ?

 

simplifying...

Find the complex zeros of each polynomial function. write f in factored form. f(x)=x^4+ 2x^3 + 22x^2 +50x- 75

x^4+ 2x^3 + 22x^2 +50x- 75=
(2x^3 +50x)+(x^4 + 22x^2 - 75)=
2x(x^2 +25)+(x^4 + 25x^2 -3x^2- 75)=
2x(x^2 +25)+(x^4 + 25x^2) -(3x^2+ 75)=
2x(x^2 +25)+x^2(x^2 + 25) -3(x^2+ 25)=
(x^2 +25)(x^2+2x-3)=
(x^2+25)(x+3)(x-1) 

zeros: {-5i, 5i, -3, 1} 



:)

Divide: (6+i)/(5-i) Write the expression in standard form.

Two complex numbers: a + bi and c + di are equal if a = c and b = d. Use that fact to solve for x and y : ( 3x -yi ) i = 6 ( 1 + yi)

( 3x -yi ) i = 6 ( 1 + yi) 
3xi+y =6+6yi 
y+3xi=6+6yi 
real:
y=6 
Imaginary: 
3x=6y=6(6)
x=12 

:)