ADD AND SUBTRACT COMPLEX NUMBERS WORKSHEET

Add and subtract complex numbers worksheet : 

Here we are going to see some practice problems on add and subtract complex numbers.

Add and subtract complex numbers worksheet - Questions

(1) Add (−3i) and (3 + 5i)

(2) Add (−6 − 2i) and (6 − 5i) 

(3) Add (5 + 6i) + (2 − 7i)

(4) Add (5 − 6i), 5i and (7 + 6i)

(5) Simplify  (−7 + 7i) − (−7 − 3i) + (−7 − 8i) 

(6) Simplify (−4 − 7i) − (4 + 5i) − (2 − i)

(7) Simplify (1 + 6i) + (6 − 2i) − (−7 + 5i)

(8) Simplify (−5 + 7i) − (−6 + i) − (−6 + 5i)

Problem 1 :

Add (−3i) and (3 + 5i)

Solution :

The first complex contains only imaginary part, but the second complex is having both real and imaginary parts.

Since there is no real part in the first complex number, we have to consider the real part as 0.

=  (−3i) + (3 + 5i)

=  (0 + 3i) + (3 + 5i)

Combining the real and imaginary parts together

=  (0 + 3) + (3i + 5i)

=  3 + 8i

Hence the answer is 3 + 8i

Problem 2 :

Add (−6 − 2i) and (6 − 5i) 

Solution :

=  (−6 − 2i) + (6 − 5i) 

=  (-6 + 6) + (-2i - 5i)

=  0 - 7i

Hence the answer is 7i.

Problem 3 :

Add (5 + 6i) + (2 − 7i)

Solution :

=  (5 + 6i) + (2 − 7i)

=  (5 + 2) + (6i - 7i)

=  7 - i

Hence the answer is 7 - i.

Problem 4 :

Add (5 − 6i), 5i and (7 + 6i)

Solution :

=  (5 − 6i) + (5i) + (7 + 6i) 

=  (5 + 7) + (-6i + 5i + 6i)

=  12 + 5i

Hence the answer is 12 + 5i.

Problem 5 :

Simplify  (−7 + 7i) − (−7 − 3i) + (−7 − 8i) 

Solution :

=  (−7 + 7i) − (−7 − 3i) + (−7 − 8i)

=  −7 + 7i + 7 + 3i  −7 − 8i

=  (-7 + 7 - 7 )+ i(7 + 3 - 8)

=  -7 + i(10 - 8)

=  -7 + 2i

Hence the answer is -7 + 2i

Problem 6 :

Simplify (−4 − 7i) − (4 + 5i) − (2 − i)

Solution :

=   (−4 − 7i) − (4 + 5i) − (2 − i)

=  −4 − 7i − 4 - 5i − 2 + i

=  (-4 -4 - 2)+ i(-7 - 5 + 1)

=  -10 + i(-12 + 1)

=  -10 - 11 i

Hence the answer is -10 - 11 i

Problem 7 :

Simplify (1 + 6i) + (6 − 2i) − (−7 + 5i)

Solution :

=  (1 + 6i) + (6 − 2i) − (−7 + 5i)

=  1 + 6i + 6 − 2i + 7 - 5i

=  (1 + 6 + 7)+ i(6 - 2 - 5)

=  14 + i(6 - 7)

=  14 - 1 i

Hence the answer is 14 - 1 i

Problem 8 :

Simplify (−5 + 7i) − (−6 + i) − (−6 + 5i)

Solution :

=  (−5 + 7i) − (−6 + i) − (−6 + 5i)

= −5 + 7i + 6 - i + 6 - 5i

=  (-5 + 6 + 6)+ i(7 - 1 - 5)

=  (12 - 5) + i(7 - 6)

=  7 +  i

Hence the answer is 7 + 1 i

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