Evaluate
900+1300i
Real Part
900
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40\times 30+40\times \left(10i\right)+30i\times 30+30\times 10i^{2}
Multiply complex numbers 40+30i and 30+10i like you multiply binomials.
40\times 30+40\times \left(10i\right)+30i\times 30+30\times 10\left(-1\right)
By definition, i^{2} is -1.
1200+400i+900i-300
Do the multiplications.
1200-300+\left(400+900\right)i
Combine the real and imaginary parts.
900+1300i
Do the additions.
Re(40\times 30+40\times \left(10i\right)+30i\times 30+30\times 10i^{2})
Multiply complex numbers 40+30i and 30+10i like you multiply binomials.
Re(40\times 30+40\times \left(10i\right)+30i\times 30+30\times 10\left(-1\right))
By definition, i^{2} is -1.
Re(1200+400i+900i-300)
Do the multiplications in 40\times 30+40\times \left(10i\right)+30i\times 30+30\times 10\left(-1\right).
Re(1200-300+\left(400+900\right)i)
Combine the real and imaginary parts in 1200+400i+900i-300.
Re(900+1300i)
Do the additions in 1200-300+\left(400+900\right)i.
900
The real part of 900+1300i is 900.
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