Engineering Board Exam Reviewer · Complex Numbers: Operations · medium

Find the real numbers x and y that satisfy (x+yi)(1+i)=3+i.

1. x=2, y=1
2. x=2, y=-1
3. x=-1, y=2
4. x=1, y=-2

Answer

B. x=2, y=-1

Solution

x+yi=3+i/1+i=(3+i)(1-i)/2=3-3i+i-i2/2=4-2i/2=2-i. So x=2 and y=-1.

More Complex Numbers: Operations questions

1. Find the roots of z2+2z+5=0.
2. Find the modulus of (3+4i)(5-12i).
3. Evaluate (1+i)8.
4. Simplify 5+5i/1-2i.
5. Simplify (3+2i)(4-5i).
6. Simplify: i2001
7. Simplify: i15+i18
8. Add: (3+5i)+(2-7i)
9. Multiply: (4+3i)(2-i)
10. Divide: 3+4i/1-2i

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