How to add complex numbers - ACT Math
Card 0 of 6
Suppose 
and 
Evaluate the following expression:
Suppose
Evaluate the following expression:
Substituting for 
and 
, we have
This simplifies to
which equals 
Substituting for
This simplifies to
which equals
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What is the sum of 
and 
given
and
?
What is the sum of
and
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
In equation 
, 
is the real component and 
is the imaginary component (designated by 
).
In equation 
, 
is the real component and 
is the imaginary component.
When added,
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
In equation
In equation
When added,
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What is the solution of the following equation?
What is the solution of the following equation?
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
First, distribute:
Then, group the real and imaginary components:
Solve to get:
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
First, distribute:
Then, group the real and imaginary components:
Solve to get:
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Complex numbers take the form 
, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number.
Simplify: 
Complex numbers take the form
Simplify:
When adding or subtracting complex numbers, the real terms are additive/subtractive, and so are the nonreal terms.
When adding or subtracting complex numbers, the real terms are additive/subtractive, and so are the nonreal terms.
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Complex numbers take the form 
, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number.
Can you add the following two numbers: 
? If so, what is their sum?
Complex numbers take the form
Can you add the following two numbers:
Complex numbers take the form a + bi, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number. Taking this, we can see that for the real number 8, we can rewrite the number as 
, where 
represents the (zero-sum) non-real portion of the complex number.
Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be 
.
Complex numbers take the form a + bi, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number. Taking this, we can see that for the real number 8, we can rewrite the number as
Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be
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Complex numbers take the form 
, where 
is the real term in the complex number and 
is the nonreal (imaginary) term in the complex number.
Which of the following is incorrect?
Complex numbers take the form
Which of the following is incorrect?
Complex numbers take the form 
, where 
is the real term in the complex number and 
is the nonreal (imaginary) term in the complex number.
Thus, to balance the equation, add like terms on the left side.
Complex numbers take the form
Thus, to balance the equation, add like terms on the left side.
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