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The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?
The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?
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Practice Questions
1 question
Q1
The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?
3 + i
3 - i
2 + 3i
2 - 3i
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z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - i^2 = 2 + 1 + i = 3 + i.
Questions & Step-by-step Solutions
1 item
Q
Q: The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?
Solution:
z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - i^2 = 2 + 1 + i = 3 + i.
Steps: 7
Show Steps
Step 1: Identify the two complex numbers. Here, z1 = 1 + i and z2 = 2 - i.
Step 2: Write down the multiplication of the two complex numbers: z1 * z2 = (1 + i)(2 - i).
Step 3: Use the distributive property (also known as the FOIL method) to multiply the two complex numbers: (1 * 2) + (1 * -i) + (i * 2) + (i * -i).
Step 4: Calculate each part: 1 * 2 = 2, 1 * -i = -i, i * 2 = 2i, and i * -i = -i^2.
Step 5: Remember that i^2 = -1, so -i^2 becomes +1.
Step 6: Combine all the parts together: 2 - i + 2i + 1.
Step 7: Combine like terms: (2 + 1) + (-i + 2i) = 3 + i.
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